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INTERNATIONA LCHEMICALSERIES 
H.  P.  TALBOT,  PH.D.,  Sc.D.,  CONSULTING  EDITOR 


PROTEINS  AND  THE  THEORY  OF 
COLLOIDAL  BEHAVIOR 


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PROTEINS 

AND  THE  THEORY  OF 

COLLOIDAL  BEHAVIOE 


BY 

JACQUES  LOEB 

MEMBER   OF  THE   ROCKEFELLER   INSTITUTE   FOR   MEDICAL   RESEARCH 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC, 
NEW  YORK:  370  SEVENTH  AVENUE 

LONDON:  6  &  8  BOUVERIE  ST.,  E,  C,  4 
1922 

C\     ,    .  A,      P 


COPYRIGHT,  1922,  BY  THE 
MCGRAW-HILL  BOOK  COMPANY,  INC. 


T  H  K    BI  A  V  I,  W     I>  R  K  S  S    YORK    PA 


PREFACE 

Colloid  chemistry  has  been  developed  on  the  assumption  that 
the  ultimate  unit  in  colloidal  solutions  is  not  the  isolated  molecule 
or  ion  but  an  aggregate  of  molecules  or  ions,  the  so-called  micella 
of  Naegeli.  Since  it  seemed  improbable  that  such  aggregates 
could  combine  in  stoichiometrical  proportions  with  acids,  alkalies, 
or  salts,  the  conclusion  was  drawn  that  electrolytes  were  adsorbed 
on  the  surface  of  colloidal  particles  according  to  a  purely  empirical 
formula,  Freundlich's  adsorption  formula. 

The  writer's  investigations  have  led  to  the  result  that  this  last 
conclusion  is  based  on  a  methodical  error,  as  far  as  the  proteins 
are  concerned ;  namely,  to  the  failure  to  measure  the  hydrogen  ion 
concentration  of  the  protein  solutions,  which  happens  to  be  one  of 
the  main  variables.  When  the  hydrogen  ion  concentrations  are 
duly  measured  and  considered,  it  is  found  that  proteins  combine 
with  acids  and  alkalies  according  to  the  stoichiometrical  laws  of 
classical  chemistry  and  that  the  chemistry  of  proteins  does  not 
differ  from  the  chemistry  of  crystalloids. 

As  long  as  chemists  continue  to  believe  in  the  existence  of  a 
special  colloid  chemistry  differing  from  the  chemistry  of  crystal- 
loids, it  will  remain  impossible  to  explain  the  physical  behavior 
of  colloids  in  general  and  of  proteins  in  particular.  This  state  of 
affairs  is  reflected  in  the  concluding  remarks  of  Burton's  interest- 
ing book  on  "The  Physical  Properties  of  Colloidal  Solutions" 
published  in  1920, 

"We  may  very  well  conclude  with  the  words  used  by  the  pioneer 
worker  Zsigmondy,  in  closing  his  first  account  of  the  early  work  on 
colloidal  solutions: 

'From  the  foregoing  outline  no  general  theory  of  colloids  can  be 
given,  for  the  study  of  colloids  has  become  a  great  and  extensive  science, 
in  the  development  of  which  many  must  assist;  only  when  the  volu- 
minous material  supplied  by  much  physico-chemical  research  has  been 
properly  systematized,  will  the  theory  of  colloidal  solutions  be  raised 
from  mere  consideration  of  the  similarities  in  special  cases  to  the  standing 
of  an  exact  science.'" 


vi  PREFACE 

Professor  F.  G.  Donnan,  of  the  University  of  London,  an- 
nounced in  1910  an  ingenious  theory  of  equilibria  which  are 
established  when  two  solutions  of  electrolytes  are  separated  by  a 
membrane  which  is  permeable  to  all  except  one  ion.  This  theory 
was  successfully  applied  by  Procter  and  Wilson  to  the  explana- 
tion of  the  influence  of  electrolytes  on  the  swelling  of  gelatin.  It 
will  be  shown  in  this  volume  that  Donnan's  theory  of  membrane 
equilibria  furnishes  a  quantitative  and  mathematical  explanation 
not  only  of  swelling  but  of  the  colloidal  behavior  of  protein  solu- 
tions in  general ;  namely,  electrical  charges,  osmotic  pressure,  vis- 
cosity, and  stability  of  suspensions.  Such  an  application  of 
Donnan's  theory  would  have  been  impossible  without  the  stoichio- 
metrical  proof  that  proteins  form  true  ionizable  salts  with  acids 
and  alkalies.  What  was  at  first  believed  to  be  a  new  type  of  chem- 
istry, namely  colloid  chemistry,  with  laws  different  from  those  of 
general  chemistry,  now  seems  to  have  been  only  an  unrecognized 
equilibrium  condition  of  classical  chemistry;  at  least  as  far  as 
the  proteins  are  concerned.  This  does  not  detract  from  the 
importance  of  colloidal  behavior  for  physiological  and  technical 
problems,  but  it  completely  changes  the  theoretical  treatment  of 
the  subject. 

Any  rival  theory  which  is  intended  to  replace  the  Donnan  theory 
must  be  able  to  accomplish  at  least  as  much  as  the  Donnan 
theory,  i.e.,  it  must  give  a  quantitative,  mathematical,  and 
rationalistic  explanation  of  the  curves  expressing  the  influence 
of  hydrogen  ion  concentration,  valency  of  ions,  and  concentration 
of  electrolytes  on  colloidal  behavior;  and  it  must  explain  these 
curves  not  for  one  property  alone  but  for  all  the  properties, 
electrical  charges,  osmotic  pressure,  swelling,  viscosity,  and 
stability  of  solution,  since  all  these  properties  are  affected  by 
electrolytes  in  a  similar  way. 

The  contents  of  the  book  are  divided  into  two  parts,  one  fur- 
nishing the  proof  of  the  stoichiometrical  character  of  the  reactions 
of  proteins,  the  second  developing  a  mathematical  and  quantita- 
tive theory  of  colloidal  behavior  on  the  basis  of  Donnan's  theory 
of  membrane  equilibria. 

The  theory  of  colloidal  behavior,  as  outlined  in  this  book,  can 
only  be  considered  as  a  first  approximation.  Finer  methods  of 
experimentation  will  have  to  be  introduced,  many  minor  dis- 


PREFACE  vii 

crepancies  will  have  to  be  accounted  for,  and  many  additions 
made.  It  was,  however,  thought  advisable  to  publish  the  book 
for  the  reason  that  the  experimental  facts  are  accumulating  so 
rapidly  that  it  is  difficult  for  anyone  to  gather  the  leading  ideas 
unless  they  are  presented  more  systematically  and  with  less 
detail  than  in  the  original  publications.  It  was  also  thought 
advisable  to  avoid  in  this  volume  a  discussion  of  the  possible 
applications  of  the  new  theory  to  physiological  and  technical 
problems. 

The  writer  wishes  to  express  his  appreciation  to  his  technical 
assistants,  Mr.  M.  Kunitz,  and  Mr.  N.  Wuest,  for  the  skill  and 
careshown  in  the  measurementsre  quired  for  the  experimental 
part  of  the  work. 

The  writer's  thanks  are  also  due  to  Dr.  John  H.  Northrop, 
Dr.  D.  I.  Hitchcock,  and  Dr.  Anne  Leonard  Loeb,  who  have  read 
part  or  all  of  the  manuscript  and  offered  valuable  suggestions; 
and  to  Dr.  J.  A.  Wilson,  who  kindly  read  and  revised  the  first 
part  of  the  chapter  on  swelling  and  suggested  to  the  writer  the 
mathematical  proof  on  page  143  of  the  book. 

The  writer  is  indebted  to  Miss  N.  Kobelt  for  the  reading  of 
the  proof  and  for  the  index. 

JACQUES  LOEB. 
THE  ROCKEFELLER  INSTITUTE  FOR 

MEDICAL  RESEARCH, 

66rn  STREET  AND  AVENUE  A; 

NEW  YORK,  N.  Y. 

March,  1922 


CONTENTS 

PAGE 
PREFACE ; .       V 

PART  I 
Proof  of  the  Stoichiometrical  Character  of  the  Reactions  of  Proteins 

CHAPTER  I 
HISTORICAL  INTRODUCTION ; 1 

1.  The  Alleged  Difference  Between  the  Chemistry  of  Colloids  and 

of  Crystalloids   .    .    ; 1 

2.  The  Isoelectric  Point  of  Proteins 6 

3.  The  Adsorption  Theory  and  the  Precipitation  of  Proteins      .    .  10 

4.  The  Hofmeister  Ion  Series 13 

5.  The  Aggregation  Hypothesis 15 

6.  Pauli's  Hydration  Theory 17 

7.  Donnan's  Membrane  Equilibrium 19 

CHAPTER  II 

QUALITATIVE  PROOF  OF  THE  CORRECTNESS  OF  THE  CHEMICAL  VIEW- 
POINT. PREPARATION  OF  PROTEINS  FREE  FROM  IONOQENIC 
IMPURITIES 27 

CHAPTER  III 

METHODS   OF   DETERMINING   THE    ISOELECTRIC   POINT   OF   PROTEIN 

SOLUTIONS 37 

CHAPTER  IV 

QUANTITATIVE  PROOF  OF  THE  CORRECTNESS  OF  THE  CHEMICAL  VIEW- 
POINT  40 

CHAPTER  V 

THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES 65 

A.  Osmotic  Pressure _. 65 

B.  Swelling 76 

C.  Viscosity 82 

ix 


X  CONTENTS 

CHAPTER  VI 

PAGE 
THE  ACTION  OF  NEUTRAL  SALTS  ON  THE  PHYSICAL  PROPERTIES  OF 

PROTEINS 88 

1.  The  Difference  in  the  Effect  of  Acids,  Alkalies,  and  Salts  on 

Proteins 88 

2.  Ion  Series  and  the  Action  of  Salts  on  Proteins 99 

CHAPTER  VII 

THE   INADEQUACY  OF  THE   PRESENT  THEORIES  OF  COLLOIDAL  BEHA- 
VIOR    112 

PART  II 

Theory  of  Colloidal  Behavior  Based  on  Donnan's  Theory  of  Membrane 

Equilibria 

CHAPTER  VIII 

MEMBRANE  POTENTIALS 120 

The  Influence  of  the  Hydrogen  Ion  Concentration  of  Gelatin 

Solutions  on  the  P.D 126 

The  Explanation  of  the  P.D.  Curve 127 

The  Valency  Effect 132 

Hydrogen  Ion  and  Chlorine  Ion  Potentials 135 

The  P.D.  of  Na  Gelatinate 137 

The  Influence  of  Neutral  Salts  on  the  P.D.  of  Gelatin  Chloride 

Solutions 139 

The  Influence  of  the  Sign  of  Charge 144 

The  Influence  of  the  Concentration  of  Protein  on  the  P.D  ...  145 

The  P.D.  of  Solutions  of  Crystalline  Egg  Albumin 145 

CHAPTER  IX 

THE  ORIGIN  OF  THE  ELECTRICAL  CHARGES  OF   MICELLES,   AND  OF 

LIVING  CELLS  AND  TISSUES 150 

1.  Stability  of  Suspensions,   Electrical  Charge  of   Micellae,   and 

Donnan  Equilibrium 150 

2.  The   Electrical  Charge  of  Suspended  Particles  of    Powdered 

Gelatin 152 

3.  The  Influence  of  pH  on  the  Charge  of  Suspended  Particles  of 

Powdered  Gelatin 155 

4.  The  Influence  of  Acid  and  Alkali  on  the  Sign  of  Charge  of 

Micellae 155 

5.  The  Influence  of  Salts  on  the  Charge  of  Suspended  Particles  of 

Gelatin .    157 

6.  The  Origin  of  the  Electrical  Charges  of  Living  Cells  and  Tis- 

sues. .    166 


CONTENTS  xi 

CHAPTER  X 

PAGE 

OSMOTIC  PRESSURE .    .  169 

1.  Theoretical  Statements 169 

2.  The  Calculated  Curves  for  the  Influence  of  pH  and  Valency     .  172 

3.  The  Influence  of  the  Addition  of  Salts 179 

4.  The  Influence  of  the  Concentration  of  a  Protein  Solution  upon 

the  Osmotic  Pressure 184 

CHAPTER  XI 
SWELLING 189 

CHAPTER  XII 

VISCOSITY 195 

CHAPTER  XIII 

A  RECIPROCAL  RELATION  BETWEEN  THE  OSMOTIC  PRESSURE  AND  THE 

VISCOSITY  OF  GELATIN  SOLUTIONS 232 

CHAPTER  XIV 

THE  STABILITY  OF  PROTEIN  SOLUTIONS 243 

A.  The  Stability  of  Aqueous  and  Alcoholic  Solutions  of  Gelatin    .   243 

CHAPTER  XV 

THE  STABILITY  OF  PROTEIN  SOLUTIONS  (CONTINUED) 266 

B.  The  Stability  of  Solutions  of  Casein  in  Water 266 

CHAPTER  XVI 

COLLOIDAL  SUBSTANCES,   COLLOIDAL  STATE,   AND  COLLOIDAL  BEHA- 
VIOR   .  ....  275 


INDEX.  287 


PROTEINS 

AND 

THE  THEORY  OF 
COLLOIDAL  BEHAVIOR 

CHAPTER  I 
HISTORICAL  INTRODUCTION 

1.  THE  ALLEGED   DIFFERENCE   BETWEEN   THE   CHEMISTRY   OF 
COLLOIDS  AND  OF  CRYSTALLOIDS 

The  distinction  between  crystalloids  and  colloids  was  proposed 
by  Graham  in  1861,  the  crystalloids  being  characterized  by  a 
tendency  to  form  crystals  when  separating  from  a  watery  solu- 
tion, and  the  colloids  by  a  tendency  to  separate  out  in  the  form 
of  " gelatinous"  (or  amorphous)  masses.  Graham  found  that 
these  two  groups  of  substances  differ  also  in  two  other  respects, 
first,  in  their  "  diffusive  mobility/'  and  second,  in  a  peculiar 
'"  physical  aggregation."  The  crystalloids  diffuse  readily  through 
different  kinds  of  membranes  (e.g.,  pig's  bladder,  parchment) 
through  which  colloids  can  diffuse  not  at  all  or  only  very  slowly. 
The  second  peculiarity  is  the  tendency  of  the  colloids  to  form 
aggregates  when  in  solution  while  this  property  is  lacking  or  less 
pronounced  in  crystalloids.  A  brief  quotation  from  a  paper  by 
Graham  will  illustrate  these  definitions: 

"  Among  the  latter  [i.e.,  the  substances  with  low  order  of  diffusibility] 
are  hydrated  silicic  acid,  hydrated  alumina,  and  other  metallic  peroxides 
of  the  aluminous  class,  when  they  exist  in  the  soluble  form;  and  starch, 
dextrin  and  the  gums,  caramel,  tannin,  albumen,  gelatine,  vegetable  and 
animal  extractive  matters.  Low  diffusibility  is  not  the  only  property 
which  the  bodies  last  enumerated  possess  in  common.  They  are 
distinguished  by  the  gelatinous  character  of  their  hydrates.  Although 

1 


2  THEORY  OF  COLLOIDAL  BEHAVIOR 

often  largely  soluble  in  water,  they  are  held  in  solution  by  a  most  feeble 
force.  They  appear  singularly  inert  in  the  capacity  of  acids  and  bases, 
and  in  all  the  ordinary  chemical  relations.1  But,  on  the  other  hand, 
their  peculiar  physical  aggregation  with  the  chemical  indifference 
referred  to,  appears  to  be  required  in  substances  that  can  intervene  in 
the  organic  processes  of  life.  The  plastic  elements  of  the  animal  body 
are  found  in  this  class.  As  gelatine  appears  to  be  its  type,  it  is  proposed 
to  designate  substances  of  the  class  as  colloids,  and  to  speak  of  their 
peculiar  form  of  aggregation  as  the  colloidal  condition  of  matter.  Opposed 
to  the  colloidal  is  the  crystalline  condition.  Substances  affecting  the 
latter  form  will  be  classed  as  crystalloids.  The  distinction  is  no  doubt 
one  of  intimate  molecular  constitution."2 

It  is  therefore  obvious  that  there  are  according  to  Graham  at 
least  two  essential  differences  between  colloids  and  crystalloids, 
the  difference  in  diffusion  through  membranes,  and  the  difference 
in  the  tendency  to  form  aggregates  in  solutions.  We  shall  see 
in  this  volume  that  the  chief  if  not  all  the  characteristics  of 
colloidal  behavior  can  be  explained  mathematically  from  the 
difference  in  diffusibility  between  colloids  and  crystalloids,  while 
the  tendency  of  the  protein  molecules  to  form  aggregates  plays 
only  an  indirect  role,  namely,  by  immobilizing  one  kind  of  ions 
without  interfering  with  the  mobility  of  other  ions. 

In  modern  colloid  chemistry  it  has,  however,  become  custom- 
ary to  consider  the  tendency  of  colloids  to  form  aggregates  as 
the  fundamental  property,  for  the  reason  that  the  precipitation 
of  colloids  was  the  chief  topic  of  research  and  discussion  in 
colloid  chemistry,  and  precipitation  is,  of  course,  due  to  the 
formation  of  aggregates.  The  colloidal  state  is  defined  by  colloid 
chemists  as  that  state  of  matter  in  which  the  ultimate  units  in 
solutions  are  no  longer  isolated  molecules  or  ions,  but  aggregates 
of  molecules  for  which  Naegeli  had  introduced  the  term  micella 
(small  crumb).  Thus  Zsigmondy  states, 

"that  the  essential  and  characteristic  constituents  of  colloidal  solutions 
are  very  small  ultramicroscopic  particles  the  dimensions  of  which  lie 
between  molecular  and  microscopic  size.  .  .  .  These  ultramicroscopic 

1  This  is  no  longer  correct,  as  we  shall  see. 

2  GRAHAM,  T.,  Phil  Trans.,  pp.  183-224,  1861.     Reprinted  in  "Chemical 
and  Physical  Researches,"  p.  553,  Edinburgh,  1876. 


HISTORICAL  INTRODUCTION  3 

particles  (ultramicrons)  have  the  same  significance  for  colloidal  solutions 
as  the  isolated  molecules  have  for  crystalloidal  solutions."1 

The  idea  that  the  ultimate  unit  of  the  colloidal  solution  is  not 
the  molecule  or  ion  of  the  solute  but  an  aggregate  induced  colloid 
chemists  to  propose  a  new  type  of  chemistry  in  which  the  laws  of 
classical  chemistry  were  replaced  by  laws  peculiar  to  colloid 
chemistry.  It  seemed  improbable  to  them  that  the  stoichio- 
metrical  laws  of  classical  chemistry  should  hold  for  colloidal 
solutions  in  which  the  ultimate  units  were  larger  aggregates  of 
molecules,  since  they  argued  that  only  the  surface  of  such  aggre- 
gates should  be  capable  of  reacting  with  other  substances.  The 
stoichiometrical  relations  valid  in  classical  chemistry  were  as  a 
consequence  replaced  in  colloid  chemistry  by  an  empirical 
formula,  Freundlich's  so-called  adsorption  formula,  which  was 
supposed  to  account  for  surface  action.2  Recent  investigations 
by  Langmuir3  have  furnished  the  proof  that  Freundlich's  adsorp- 
tion formula  does  not  hold  for  the  reaction  of  gases  with  mica, 
glass,  and  platinum  possessing  a  smooth  surface,  and  Langmuir 
was  able  to  show  that  the  forces  which  act  in  these  cases  are  the 
purely  chemical  forces  of  primary  or  secondary  valency.  Like 
most  empirical  formulas  the  adsorption  formula  may  hold  within 
a  limited  range  of  observations,  but  not  throughout  the  whole 
range  of  variation,  and  Langmuir  states  that  this  was  also  true 
for  the  adsorption  formula  in  his  experiments. 

John  A.  Wilson  and  Wynnaretta  H.  Wilson4  have  made  a  most 
important  contribution  towards  the  question  of  the  applicability 
of  the  adsorption  formula  to  colloidal  problems,  in  which  they 
were  also  led  to  a  rejection  of  the  adsorption  formula  and  to  the 
adoption  of  a  purely  chemical  interpretation.  Their  discussion 
is  based  on  the  experiments  of  Procter  and  Wilson  on  gelatin 
and  the  facts  to  be  given  in  this  book  fully  support  their  skeptical 
attitude  towards  the  adsorption  formula. 

Even  if  we  assume  that  the  protein  solutions  contain  no  free 
protein  ions  or  molecules — which  is  contradicted  by  the  experi- 

1  ZSIGMONDY,  R.,  "Kolloidchemie,"  2nd  ed.,  Leipsic,  1918. 

2  FREUNDLICH,  H.,  "  Kapillarchemie,"  Leipsic,  1909. 
'LANGMUIR,  I.,  J.  Am.  Chem.  Soc.,  vol.  40,  p.  1361,  1918. 

4  WILSON,  J.  A.  and  WILSON,  W.  H.,  J.  Am.  Chem.  Soc.,  vol.  40,  p.  886, 
1918. 


4  THEORY  OF  COLLOIDAL  BEHAVIOR 

ments  on  potential  difference  and  osmotic  pressure  to  be  dis- 
cussed later — such  an  assumption  does  not  lead  to  the  idea  that 
chemical  reactions  occur  only  at  the  surface  of  the  micellae  for 
the  simple  reason  that  solid  gels  of  proteins  (e.g.,  of  gelatin)  are 
easily  permeable  to  acids,  alkalies,  and  salts  or  to  crystalloids  in 
general.  Chemical  reactions  are,  therefore,  not  restricted  to  the 
surface  of  protein  micellse. 

While  a  number  of  authors,  like  Bugarszky  and  Liebermann,1 
Osborne,2  Robertson,3  Pauli,4  and  others  assumed  that  the  reac- 
tions of  proteins  are  purely  chemical,  this  assumption  could  not 
be  proved  conclusively  until  the  modern  methods  of  measuring 
the  hydrogen  ion  concentration  of  protein  solutions  were 
developed  by  Friedenthal,  S^rensen,5  Michaelis,6  Clark,7  and 
their  collaborators.  On  the  basis  of  these  methods  it  was  easy 
to  demonstrate  the  purely  stoichiometrical  character  of  the 
combination  of  proteins  with  acids  and  alkalies. 

Thus  it  was  proved  that  gelatin  combines  with  acids  only  when 
the  hydrogen  ion  concentration  of  the  solution  is  above  a  certain 
critical  point,  namely  greater  than  N/50,000  (or  pH  =  4.7).* 
At  hydrogen  ion  concentrations  above  N/50,000,  H3PO4  dis- 
sociates as  a  monobasic  acid.  Hence,  if  gelatin  combines  stoichio- 
metrically  with  acids  it  should  require  three  times  as  many 
cubic  centimeters  of  0.1  N  H3PO4  as  it  requires  cubic  centimeters 
of  0.1  N  HC1  or  HNO3  to  bring  1  gm.  of  gelatin  in  100  cc.  solution 
from  a  hydrogen  ion  concentration  of  N/50,000  to  that  of,  e.g., 
N/1,000.  The  strong  acid  H2SO4  dissociates,  however,  in  this 

1  BUGARSZKY,  S.  and  LIEBERMANN,  L.,  Arch.  ges.   PhysioL,  vol.  72,  p.  51, 
1898. 

2  OSBORNE,  T.  B.,  Die  Pflanzenproteine :  Ergeb.  PhysioL,  vol.  10,  p.  47, 
1910. 

3  ROBERTSON,  T.  B.  "The  Physical  Chemistry  of  the  Proteins,"  New  York, 
London,  Bombay,  Calcutta,  and  Madras,  1918. 

4  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912.     "Kol- 
loidchemie  der  Eiweisskorper,"  Dresden  and  Leipsic,  1920. 

6  S0RENSEN,  S.  P.  L.,  see  Bibliography  given  in  W.  M.  CLARK,  "The 
Determination  of  Hydrogen  Ions,"  Baltimore,  1920. 

6  MICHAELIS,   L.,    "Die    Wasserstoffionenkonzentration,"    Berlin,    1914. 

7  CLARK,  W.  M.,  "The  Determination  of  Hydrogen  Ions,"  Baltimore, 
1920. 

8  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  85,  1920-21.     Science,  vol.  52,  p.  449, 
1920.     J.  chim.  physique,  vol.  18,  p.  283,  1920. 


HISTORICAL  INTRODUCTION  5 

range  of  hydrogen  ion  concentration  as  a  dibasic  acid  and  hence,  it 
should  require  as  many  cubic  centimeters  of  0.1  N  H2SO4  as  it 
requires  cubic  centimeters  of  0.1  N  HC1  to  bring  the  same  1  per 
cent  solution  of  gelatin  from  a  hydrogen  ion  concentration  of 
N/50,000  to  one  of  N/1,000.  Titration  experiments  proved  the 
correctness  of  these  and  similar  conclusions,  not  only  in  the  case 
of  gelatin  but  also  of  other  proteins,  thus  leaving  no  doubt  that 
proteins  combine  with  acids  or  alkalies  according  to  the  stoichio- 
metrical  laws  of  general  chemistry.1 

It  was  merely  an  unfortunate  historical  accident  that  the 
colloidal  behavior  of  proteins  was  investigated  before  the  con- 
venient methods  of  measuring  the  hydrogen  ion  concentration 
were  developed;  otherwise,  we  should  probably  never  have  heard 
of  the  idea  that  the  chemistry  of  colloids  differs  from  the  chemistry 
of  crystalloids,  at  least  as  far  as  the  proteins  are  concerned.  It 
was  this  methodical  error  of  not  measuring  the  hydrogen  ion 
concentration  of  colloidal  solutions  and  of  gels  which  prevented 
the  development  of  an  exact  theory  of  colloidal  behavior  and 
which  gave  rise  to  the  statement  of  Zsigmondy  quoted  in  the 
preface. 

The  reason  that  measurements  of  the  hydrogen  ion  concentra- 
tion are  paramount  for  the  understanding  of  the  chemical  and 
physical  behavior  of  the  proteins  lies  in  the  fact  that  proteins  are 
amphoteric  electrolytes  capable  of  forming  ionizable  salts  with 
acids  as  well  as  with  alkalies,  according  to  the  hydrogen  ion 
concentration.  When  the  hydrogen  ion  concentration  exceeds  a 
certain  critical  value  (which  varies  for  different  proteins)  the 
protein  behaves  as  if  it  were  a  base,  like  NH3,  capable  of  forming 
salts  with  acids;  while  when  the  hydrogen  ion  concentration  of 
the  solution  is  below  this  critical  value  the  protein  behaves  as 
if  it  were  a  fatty  acid,  e.g.,  CH3COOH,  capable  of  forming  salts 
with  bases.  At  the  critical  value  of  the  hydrogen  ion  concentra- 
tion the  protein  can  practically  combine  neither  with  an  acid  nor 
a  base  nor  a  neutral  salt.2  This  critical  hydrogen  ion  concen- 
tration is  called  the  "  isoelectric "  point  of  the  protein.  More- 
over, we  shall  see  that  the  fraction  of  1  gm.  of  originally  isoelectric 

1  LOEB,  J.,  J.  Gen.  Physiol,  vol.  3,  pp.  85,  547,  1920-21. 

2  LOEB,  J.,  J.  Gen.  Physiol.,  vol.  1,  pp.  39,  237,  1918-19.     Science,  vol.  52, 
p.  449,  1920,  /.  chim.  physique,  vol.  18,  p.  283,  1920. 


6  THEORY  OF  COLLOIDAL  BEHAVIOR 

protein  in  100  c.c.  solution  capable  of  combining  with  an  acid  or 
alkali,  is  also  a  definite  function  of  the  hydrogen  ion  concentration. 

2.  THE  ISOELECTRIC  POINT  OF  PROTEINS 

The  conception  of  the  "isoelectric  point"  of  proteins  was 
introduced  before  its  chemical  meaning  was  recognized  and  it 
attracted  attention  because  it  was  connected  with  the  precipita- 
tion of  colloids,  a  phenomenon  on  which  the  interest  of  a  number 
of  investigators  had  been  focussed.  The  conception  of  the 
isoelectric  point  of  proteins,  which  is  due  to  W.  B.  Hardy,1 
must  be  considered  as  the  starting  point  for  the  physical  chem- 
istry of  proteins.  This  author  found  in  1899  that  white  of  egg 
diluted  with  eight  or  nine  times  its  volume  of  distilled  water, 
filtered,  and  boiled  when  put  into  an  electrical  field  migrated 
in  an  opposite  direction  according  to  whether  the  reaction  of  the 
fluid  was  acid  or  alkaline.  When  the  fluid  had  an  alkaline 
reaction,  the  particles  moved  in  an  electrical  field  from  the 
cathode  to  the  anode;  when  the  fluid  was  acid,  the  direction  of  the 
motion  of  the  particles  was  the  reverse,  namely,  from  the  anode 
to  the  cathode;  when  the  fluid  was  neutral  the  movement  of  the 
particles  under  the  influence  of  a  current  was  so  slight  that  it  was 
difficult  to  detect. 

"I  have  shown  that  the  heat-modified  proteid  is  remarkable  in  that  its 
direction  of  movement  [in  an  electric  field]  is  determined  by  the  reaction 
acid  or  alkaline,  of  the  fluid  in  which  it  is  suspended.  An  immeasurably 
minute  amount  of  free  alkali  causes  the  proteid  particles  to  move  against 
the  stream  while  in  presence  of  an  equally  minute  amount  of  free  acid 
the  particles  move  with  the  stream.  In  the  one  case  therefore  the 
particles  are  electro-negative,  in  the  other  they  are  electro-positive. 
Since  one  can  take  a  hydrosol  in  which  the  particles  are  electro-negative 
and,  by  the  addition  of  free  acid,  decrease  their  negativity,  and  ulti- 
mately make  them  electro-positive  it  is  clear  that  there  exists  some 
point  at  which  the  particles  and  the  fluid  in  which  they  are  immersed 
are  isoelectric. 

"The  isoelectric  point  is  found  to  be  one  of  great  importance.  As  it 
is  neared  the  stability  of  the  hydrosol  diminishes  until,  at  the  isoelectric 
point,  it  vanishes,  and  coagulation  or  precipitation  occurs,  the  one  or  the 
other  according  to  whether  the  concentration  of  the  proteid  is  high  or 

1  HARDY,  W.  B.,  Proc.  Roy.  Soc.,  vol.  66,  p.  110,  1900. 


HISTORICAL  INTRODUCTION  7 

low,  and  whether  the  isoelectric  point  is  reached  slowly  or  quickly, 
and  without  or  with  mechanical  agitation." 

In  a  preliminary  note1  on  his  work  on  globulins  published  in 
1903  Hardy  gives  an  interpretation  of  the  influence  of  H  and  OH 
ions  on  the  direction  of  migration  of  protein  particles  in  an 
electrical  field  which  was  destined  to  play  an  important  role  in 
colloid  chemistry,  since  it  suggested  to  the  later  workers  that  the 
H  and  OH  ions  produced  their  influence  on  the  electrical  charge  of 
the  protein  particles  through  a  process  of  adsorption. 

"The  properties  of  globulins  in  solution  seem  to  justify  the  following 
view:  They  are  not  embraced  by  the  theorem  of  definite  and  multiple 
proportions.  Therefore  they  are  conditioned  by  purely  chemical  forces 
only  in  a  subsidiary  way.  A  precipitate  of  globulin  is  to  be  conceived 
not  as  composed  of  molecular  aggregates  but  of  particles  of  gel.  I  have 
shown  elsewhere  that  gelation  and  precipitation  of  colloidal  solutions 
are  continuous  processes.  These  particles  of  gel  when  suspended  in  a 
fluid  containing  ions  are  penetrated  by  those  ions.  Let  the  fundamental 
assumption  be  that  the  higher  the  specific  velocity  of  an  ion  the  more 
readily  it  will  become  entangled  within  the  colloidal  particle.  Then 
as  H  and  OH  ions  have  by  far  the  highest  specific  velocity  the  colloidal 
particle  will  entangle  an  excess  of  H  ions  in  acid  and  thereby  acquire  a 
+  charge  and  of  OH  ions  in  alkali  and  thereby  acquire  a  —  charge. 
These  charges  will  decrease  the  surface  energy  of  the  particle  and 
thereby  lead  to  changes  in  their  average  size." 

Perrin  adopted  the  idea  that  H  and  OH  ions  confer  their 
electrical  charge  to  colloidal  particles  on  account  of  their  rela- 
tively large  velocity  of  migration,  whereby  they  were  readily 
adsorbed  by  the  colloidal  particle.  The  hypothesis  of  a  prefer- 
ential adsorption  of  H  and  OH  ions  by  colloidal  particles  has 
since  played  a  great  role  in  colloid  chemistry. 

In  1904  the  writer  of  this  volume  offered  instead  of  this  colloidal 
a  purely  chemical  view  of  the  significance  of  the  isoelectric 
point  and  of  the  cause  of  the  influence  of  acids  and  alkalies  on 
the  direction  of  the  migration  of  the  colloidal  particles.2 

"It  seems  to  the  writer,  however,  that  a  different  view  of  these 
phenomena  is  possible  whereby  they  appear  in  harmony  with  the  view 
of  electrolytic  origin  of  the  charges  of  colloids.  The  proteids  are  known 

1  HARDY,  W.  B.,  J.  Physiol.,  vol.  29,  p.  29,  1903. 

2  LOEB,  J.,  Univ.  of  Cal  Publications,  Physiology,  vol.  1,  p.  149,  1904. 


8  THEORY  OF  COLLOIDAL  BEHAVIOR 

to  be  amphoteric  in  their  reaction.  If  they  be  slightly  dissociable  they 
will  send  H  as  well  as  OH  ions  into  the  solution.  When  the  particles 
send  more  H  ions  than  OH  ions  into  the  solution  they  will  have  a 
negative  charge  while  they  will  have  a  positive  charge  when  more  OH 
ions  are  given  off  than  H  ions.  If  acid  is  added  to  the  solution  in  suffi- 
cient concentration  the  amphoteric  colloidal  particle  will  send  more  OH 
ions  into  the  solution  than  H  ions  and  hence,  will  assume  a  positive 
charge.  The  reverse  will  be  the  case  in  an  alkaline  solution.  It 
harmonizes  with  this  idea  that,  as  Hardy  found,  neutral  salts  do  not 
influence  the  sign  of  the  electrical  charge  of  the  globulins." 

We  shall  see  later  on  that  this  suggestion  explains  the  source  of 
the  electrical  charge  of  isolated  protein  ions  but  explains  only 
indirectly  the  charge  of  larger  aggregates. 

In  his  famous  paper  on  " Colloidal  Solution"  published  in 
1905,  Hardy1  abandons  the  physical  view  which  he  expressed  in 
1903  and  adopts  "a  frankly  chemical  standpoint." 

"  Globulin  therefore  is  an  amphoteric  substance  and  its  acid  function 
is  much  stronger  than  its  basic  function.  As  an  acid  it  is  strong  enough 
to  form  salts  readily  with  bases  so  weak  as  aniline,  glycocoll,  and  urea; 
acting  as  a  base  it  forms  salts  with  weak  acids,  such  as  acetic,  and  boracic 
acids,  which  are  very  unstable  in  presence  of  water." 

While  Hardy  accepts  the  idea  of  an  electrolytic  origin  of  the 
charges  of  proteins,  he  does  not  seem  to  be  ready  to  concede  that 
the  reactions  of  proteins  with  acids  and  alkalies  are  purely 
stoichiometric,  as  the  following  quotations  indicate. 

"  Though  one  may  speak  of  the  colloid  particles  as  being  ionic  in 
nature  they  are  sharply  distinct  from  true  ions  in  the  fact  that  they  are 
not  of  the  same  order  of  magnitude  as  are  the  molecules  of  the  solvent, 
the  electric  charge  which  they  carry  is  not  a  definite  multiple  of  a  fixed 
quantity  and  one  cannot  ascribe  to  them  a  valency,  and  their  electrical 
relations  are  those  which  underlie  the  phenomena  of  electrical  endosmose. 
To  such  ionic  masses  I  would  give  the  name  'pseudo-ions'  and  I  propose 
to  treat  globulin  solutions  from  the  standpoint  of  a  hypothesis  of 
'pseudo-ions.'2 

And  in  1910  Wood  and  Hardy3  express  the  view  that  proteins 

1  HARDY,   W.   B.,  J.    Physiol.,    vol.    33,    p.    251,    1905-06.      See    also, 
HARDY,  W.  B.,  Proc.  Roy.  Soc.,  vol.  79,  p.  413,  1907. 

2  HARDY,  W.  B.,  J.  Physiol.,  vol.  33,  pp.  256-257,  1905-06. 

3  WOOD,  T.  B.  and  HARDY,  W,  B.,  Proc,  Roy.  Soc.,  vol  81,  p.  38,  1909, 


HISTORICAL  INTRODUCTION  9 

"react  with  acids  and  alkalies  to  form  salts,  but  the  reactions  are  not 
precise,  an  indefinite  number  of  salts  of  the  form  (B)«BHA  being  formed 
where  the  value  of  n  is  determined  by  conditions  of  temperature  and 
concentration,  and  of  inertia  due  to  electrification  of  internal  surfaces 
within  the  solution." 

There  are  two  elements  in  this  view  which  should  be  separated. 
The  suggestion  that  the  electrical  charges  of  the  micellae  are  not 
"a  definite  multiple  of  a  fixed  quantity"  harmonizes  with  the 
results  to  be  given  later.  The  other  suggestion,  however,  "that 
the  reactions  are  not  precise"  seems  to  be  contradicted  by  the 
stoichiometrical  facts  to  be  enumerated  in  the  fourth  chapter. 

When  the  methods  of  measuring  the  hydrogen  ion  concentra- 
tion had  been  developed  by  H.  Friedenthal  and  by  S^rensen  it 
became  possible  to  determine  the  isoelectric  point  of  genuine 
proteins.  This  was  first  done  by  Michaelis  and  his  collaborators 
in  1910.  Michaelis  used  the  same  method  of  migration  of  the 
particles  in  an  electrical  field  which  had  been  used  by  Hardy. 
The  isoelectric  point  is,  according  to  Michaelis,  that  hydrogen 
ion  concentration  at  which  the  particles  migrate  neither  to  the 
anode  nor  to  the  cathode.  The  following  figures  give  the 
hydrogen  ion  concentrations  defining  the  isoelectric  points  of 
different  proteins  as  determined  by  Michaelis.1 

Genuine  serum  albumin 2      X  10~5N 

Genuine  serum  globulin 4      X  10~6N 

Oxyhemoglobin 1.8  X  10~7N 

Gelatin 2     X  10~5N 

Casein 2      X  10~6N 

According  to  S^rensen  the  isoelectric  point  of  crystalline  egg 
albumin  is  near  that  of  serum  albumin  (namely,  at  a  pH  of  4.8). 2 

We  shall  denote  in  this  book  the  hydrogen  ion  concentration 
by  S^rensen's  logarithmic  symbol  pH;  e.g.,  the  concentration 
2  X  10~5N  =  10~4-7N  is  written  merely  pH  4.7,  the  minus  sign 
being  omitted. 

If  we  assume  that  the  ultimate  units  of  a  protein  solution  are 
as  a  rule  isolated  protein  molecules  or  ions  which  react  stoichi- 

1  MICHAELIS,  L.,  "Die  Wasserstoffionenkonzentration,"  p.  54  ff,  Berlin, 
1914. 

2  S0RENSEN,  S.  P.  L.,  Studies  on  proteins:  Compt.  rend.  trav.  Lab.  Carls- 
berg,  vol.  12,  Copenhagen,  1915-17. 


10  THEORY  OF  COLLOIDAL  BEHAVIOR 

ometrically  with  acids  and  alkalies,  forming  highly  dissociable 
metal  proteinates  or  protein-acid  salts,  we  may  define  the  iso- 
electric  point  of  a  protein  as  that  hydrogen  ion  concentration 
in  which  the  protein  exists  practically  in  a  non-ionogenic  (or  non- 
ionized)  condition  being  able  to  form  practically  neither  metal 
proteinate  nor  protein-acid  salt.  We  shall  see  that  this  theo- 
retical result  leads  to  a  simple  practical  method  of  preparing 
proteins  entirely  or  practically  free  from  ionogenic  impurities. 
The  fact  that  solutions  and  suspensions  of  proteins  are  least 
stable  at  the  isoelectric  point  is  then  connected  with  the  purely 
chemical  fact  that  proteins  are  amphoteric  electrolytes  which 
exist  at  their  isoelectric  point  in  the  form  of  practically  non- 
ionizable  protein  molecules. 

3.  THE    ADSORPTION    THEORY    AND    THE    PRECIPITATION    OF 

PROTEINS 

The  interest  of  most  investigators  of  colloidal  phenomena  was 
centered  on  the  precipitation  of  colloids,  especially  in  those  cases 
where  the  precipitation  required  low  concentrations  of  electro- 
lytes. The  explanation  accepted  by  the  majority  of  authors  is 
based  on  the  assumption  of  an  adsorption  of  ions  by  the  colloid. 

Hardy  explained  his  discovery  that  proteins  are  most  easily 
flocculated  from  their  solutions  at  the  isoelectric  point  by  the 
fact  that  at  that  point  the  electrical  charges  of  the  protein  particles 
are  a  minimum,  a  conclusion  derived  from  his  observation  that  at 
the  isoelectric  point  proteins  do  not  migrate  in  an  electrical 
field.  He  concluded  from  this  that  the  stability  of  colloidal 
solutions  is  due  to  the  potential  difference  between  each  colloidal 
particle  and  the  surrounding  liquid.  In  this  state  the  charged 
particles  must  repel  each  other  with  the  result  that  they  become 
evenly  distributed  through  the  solvent.  When  the  charge  is 
annihilated  or  sufficiently  diminished  "the  adhesion  or  'idio- 
attraction'  as  Graham  called  it,  of  the  colloid  particles  for  each 
other  makes  them  cohere  where  they  come  together."1  He 
originally  assumed  the  positive  charge  of  the  particles  in  the 
acid  solution  to  be  due  to  a  preferential  adsorption  of  H  ions 
and  the  negative  charge  in  the  presence  of  alkali  to  the  adsorption 

1  WOOD,  T.  B.  and  HARDY,  W.  B.,  Proc.  Roy.  Soc.,  vol.  81,  p.  41,  1909. 


HISTORICAL  INTRODUCTION  11 

of  OH  ions.  Later  he  abandoned  this  view,  which,  however, 
is  still  held  by  many  chemists. 

Another  explanation  of  the  coalescence  of  the  particles  which 
have  lost  their  electrical  charge  was  given  by  Bredig  on  the  basis 
of  surface  tension  changes.  The  surface  tension  at  the  boundary  of 
a  micella  and  water  is  diminished  when  the  particles  are  elec- 
trically charged  and  reaches  a  maximum  when  the  charge  is 
annihilated.  Since  at  the  isoelectric  point  the  electrical  charges 
of  the  particles  are  nil  the  surface  tension  at  the  boundary  of 
particles  and  water  must  be  a  maximum  and  as  a  consequence 
two  isoelectric  particles  upon  coming  in  contact  are  forced  to 
coalesce;  while  the  particles  will  not  coalesce  when  the  surface 
tension  is  low.1 

It  is,  however,  doubtful  whether  the  coalescence  of  the  non- 
charged  colloidal  particles  is  due  to  surface  tension  effects. 
Zsigmondy2  points  out  that  Powis'3  observations  on  the  precipi- 
tation of  droplets  of  oil  emulsion  by  salts  make  it  more  probable 
that  the  coalescence  is  due  to  forces  of  attraction  between  the 
droplets,  since  in  commencing  flocculation  the  individual  oil 
globules  only  adhere  to  each  other  without  coalescing  into  larger 
droplets. 

Colloids  can,  however,  be  flocculated  by  salts  even  if  their  solu- 
tion is  not  at  the  isoelectric  point.  In  this  case  Hardy  assumes 
that  the  addition  of  the  salt  lowers  the  potential  difference 
between  the  colloidal  particle  and  the  solvent.  Schulze,  Linder 
and  Picton,  as  well  as  Hardy4  had  found  that  the  ion  which  is 
responsible  for  the  flocculation  has  always  the  opposite  sign  of 
charge  to  the  colloidal  particle,  and  moreover,  that  the  coagulative 
power  of  the  ion  increases  rapidly  with  its  valency.5  This  rule 
was  considered  to  strengthen  the  adsorption  theory. 

It  was  assumed  that  the  micellse  possess  an  electrical  charge 

1  MICHAELIS,  L.,  "Die  Wasserstoffionenkonzentration,"  pp.  49-50,  Berlin, 
1914. 

2  ZSIGMONDY,  R.,  "Kolloidchemie,"  2nd  ed.,  p.  63,  Leipsic,  1918. 

3  Powis,  F.,  Z.  physik.  Chem.,  vol.  89,  pp.  91,  179,  186,  1915. 

4  HARDY,  W.  B.,  Proc.  Roy.  Soc.,  vol.  66,  p.  110,  1900,  J.  Physiol,  vol. 
33,  p.  251,  1905-06. 

6  For  the  details  and  the  literature  see  BURTON,  E.  F.,  "The  Physical 
Properties  of  Colloidal  Solutions,"  2nd  ed.,  London,  New  York,  Bombay, 
Calcutta,  and  Madras,  1921. 


12  THEORY  OF  COLLOIDAL  BEHAVIOR 

which  will  cause  them  to  " adsorb"  most  readily  those  ions  of  an 
electrolyte  which  have  the  opposite  sign  of  charge  from  the 
colloidal  particle.  This  adsorption  is  supposed  to  annihilate  the 
charge  of  the  particles  causing  them  to  coalesce.  The  higher  the 
charge  of  the  ion  the  more  readily  it  is  adsorbed;  and  this  is 
presumed  to  explain  why  the  flocculating  action  of  ions  increases 
with  their  valency.1 

The  hypothesis  that  the  electrical  charges  of  micellae  of  proteins 
are  diminished  or  annihilated  by  the  preferential  adsorption  of 
the  ions  of  a  salt  rests  on  no  measurements  and  the  hypothesis 
has  never  advanced  beyond  the  stage  of  vague  qualitative  specu- 
lation. Such  speculations  would  never  have  been  accepted  or 
considered  if  it  were  not  for  the  fact  that  there  existed  no  direct 
measurements  of  the  charges  of  suspended  protein  particles. 
The  writer  found  a  method  of  directly  measuring  the  P.D.  between 
protein  particles  and  surrounding  liquid,  and  was  thus  able  to 
follow  minutely  the  influence  of  the  hydrogen  ion  concentration 
and  of  the  addition  of  salts  on  the  P.D.2  The  quantitative  data 
thus  gained  made  it  possible  to  investigate  the  origin  of  the 
P.D.  and  it  was  found  that  this  P.D.  is  due  to  the  fact  that  proteins 
form  ionizable  salts  with  acids  and  bases.  Whenever  protein 
ions  are  prevented  from  diffusing  through  membranes  or  gels 
permeable  to  crystalloidal  ions,  peculiar  equilibrium  conditions 
are  established  resulting  in  an  unequal  distribution  of  the 
oppositely  charged  crystalloidal  ions  between  colloidal  particle 
and  surrounding  liquid.  This  unequal  distribution  of  oppositely 
charged  ions  leads  to  the  P.D.  at  the  boundary  of  micellae  and 
surrounding  liquid.  It  is  possible  to  explain  mathematically, 
from  Donnan's  equation  for  such  membrane  equilibria,  the  influ- 
ence of  acids,  alkalies,  and  neutral  salts  on  the  charges  of  the 
micellae,  and  it  can  be  shown  that  the  observed  P.D.  agrees 
quantitatively  with  that  calculated  from  the  equilibrium  equation. 
It  thus  turns  out  that  the  explanation  of  the  annihilation  of  the 

1  For  a  full  presentation  of  the  adsorption  theory  the  reader  is  referred  to 
BANCROFT,  W.  D.,  "  Applied  Colloid  Chemistry,"  New  York,  London,  1921, 
in  this  series,  and  to  LEWIS,  W.  C.  McC.,  "A  System  of  Physical  Chemistry," 
2nd  ed.,  vol.  1,  p.  346,  London,  New  York,  Bombay,  Calcutta,  and  Madras, 
1920. 

aLoEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  667,  1920-21;  vol.  4,  p.  351,  1921-22. 


HISTORICAL  INTRODUCTION  13 

charges  of  micellae  by  neutral  salts  depends  on  the  fact  that 
proteins  combine  stoichiometrically  with  acids  and  alkalies 
forming  true  ionizable  salts.  The  agreement  between  calculated 
and  observed  values  is  so  close  that  there  is  neither  any  need  nor 
room  for  speculations  on  adsorption,  unless  it  can  be  shown  that 
the  adsorption  hypothesis  furnishes  an  equally  good  mathematical 
and  quantitative  agreement  between  observed  and  calculated 
P.D. 

4.  THE  HOFMEISTER  ION  SERIES 

Hofmeister1  was  the  first  to  investigate  the  effects  of  different 
salts  on  the  physical  properties  of  proteins.  He  and  his  followers 
observed  that  the  relative  effects  of  anions  on  the  precipitation, 
the  swelling,  and  other  properties  of  proteins  seemed  very  definite 
and  that  the  anions  could  be  arranged  apparently  in  definite 
series  according  to  their  relative  efficiency,  the  order  being 
independent  of  the  nature  of  the  cation.  Similar  series  were  also 
found  for  the  cations,  though  these  series  seemed  to  be  less 
definite.  These  Hofmeister  series  were  a  puzzle  to  those  who 
accepted  the  chemical  viewpoint  of  the  behavior  of  proteins,  inas- 
much as  it  was  impossible  to  discover  in  these  series  a  relation  to 
the  typical  combining  ratios  of  the  ions. 

To  illustrate  this  we  will  quote  the  order  which,  according  to 
Pauli,2  represents  the  relative  efficiency  of  different  acids  on  the 
viscosity  of  blood  albumin, 

HC1  >  monochloracetic  >  oxalic  >  dichloracetic  > 
citric  >  acetic  >  sulphuric  >  trichloracetic  acid, 

where  HC1  increased  the  viscosity  most  and  trichloracetic  or 
sulphuric  least.  In  this  series  the  strong  monobasic  acid  HC1  is 
followed  by  the  weak  monochloracetic  acid,  this  is  followed  by 
the  dibasic  oxalic  acid ;  later  follows  the  weak  tribasic  citric  acid, 
then  the  very  weak  monobasic  acetic  acid,  then  the  strong  dibasic 
sulphuric  acid,  and  finally  again  a  monobasic  acid,  trichloracetic. 
According  to  Hofmeister,  gelatin  swells  more  in  chlorides, 

1  HOFMEISTER,  F.,  Arch.  exp.   Path.  u.   Pharm.,   vol.    24,  p.  247,  1888; 
vol.  25,  p.  1,  188&-89;  vol.  27,  p.  395,  1890;  vol.  28,  p.  210,  1891. 

2  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912. 


14  THEORY  OF  COLLOIDAL  BEHAVIOR 

bromides,  and  nitrates  than  in  water,  while  in  acetates,  tartrates, 
citrates,  or  sugar  it  swells  less  than  in  water.  R.  S.  Lillie1  arranges 
ions  according  to  their  depressing  effect  on  the  osmotic  pressure 
of  gelatin  solution  in  the  following  way: 

Cl>S04>N03>Br>I>CNS 

These  series2  again  betray  no  relation  to  the  stoichiometrical 
properties  of  the  ions.  As  long  as  these  Hofmeister  ion  series 
were  believed  to  have  a  real  existence  it  seemed  futile  to  decide 
for  or  against  a  purely  chemical  theory  of  the  behavior  of  colloids 
since  even  with  a  bias  in  favor  of  a  chemical  theory  the  Hof- 
meister series  remained  a  riddle. 

The  writer  believes  that  he  has  removed  these  difficulties  by 
using  protein  solutions  of  equal  hydrogen  ion  concentration  as 
the  standard  of  comparison. 

In  this  way  it  was  found  that  a  number  of  authors  had  errone- 
ously attributed  the  effects  of  an  alteration  of  the  hydrogen  ion 
concentration  upon  the  physical  properties  of  a  protein  to  a 
difference  in  the  specific  action  of  the  anion  or  cation  added. 
Thus  it  was  always  believed  that  acetates  have  almost  as  great  a 
"dehydrating"  action  as  sulphates,  but  it  was  overlooked  that 
acetic  acid  is  a  weak  acid,  and  that  in  the  experiments  referred  to 
the  authors  failed  to  compare  the  effects  of  SO4  and  CH3COO  at 
the  same  hydrogen  ion  concentration.  When  this  error  is 
avoided  it  can  be  shown  that  acetates  influence  the  swelling, 
osmotic  pressure,  and  viscosity  of  protein  solutions  in  the  same 
way  as  chlorides  or  nitrates,  but  not  in  the  same  way  as  sulphates; 
in  other  words,  anions  of  the  same  valency  act  alike.3 

By  taking  into  consideration  the  hydrogen  ion  concentration 
it  was  possible  to  show  that  the  assumption  of  specific  differences 
in  the  action  of  different  ions  of  the  same  valency  and  sign  of 
charge  was  due  to  a  methodical  error;  and  that  the  Hofmeister 
rule  must  be  replaced  by  a  simple  valency  rule,  according  to 
which  only  the  valency  and  sign  of  charge  of  an  ion  influence  the 
colloidal  behavior  of  a  protein  but  that  the  other  properties  of 

1  LILLIE,  R.  S.,  Am.  J.  PhysioL,  vol.  20,  p.  127,  1907-08. 

2  A  fuller  discussion  of  these  series  is  found  in  HOBER,  R.,  " Physikalische 
Chemie  der  Zelle  und  der  Gewebe,"  Leipsic  and  Berlin,  1914. 

3LoEB,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  391,  1920-21. 


HISTORICAL  INTRODUCTION  15 

the  ion  have  no  influence  as  long  as  no  constitutional  change  in 
the  protein  molecule  occurs. 

This  fact  established  a  complete  harmony  between  the  results 
of  the  titration  experiments  and  the  influence  of  ions  on  the  phys- 
ical properties  of  gelatin.  In  the  titration  experiments  it  had 
been  found  that  at  a  hydrogen  ion  concentration  of  above  2  X 
10~5N  weak  dibasic  or  tribasic  acids  generally  combine  with  a 
protein  as  if  they  were  entirely  or  chiefly  monobasic.  Hence,  the 
anions  of  the  protein  salts  formed  with  these  weak  dibasic  or 
tribasic  acids,  e.g.,  phosphoric,  citric,  tartaric,  succinic,  were 
monovalent,  and  it  was  found  that  the  osmotic  pressure  or 
viscosity  of  solutions  of  protein  phosphates  were  the  same  as 
those  of  protein  chlorides  for  the  same  hydrogen  ion  concentration 
and  the  same  concentration  of  originally  isoelectric  protein. 

On  the  other  hand,  the  titration  experiments  showed  that  the 
anion  of  protein  sulphate  is  dibasic  and  it  was  found  that  the  os- 
motic pressure  and  viscosity  of  protein  sulphate  is  less  than  one-half 
of  that  of  protein  chloride  or  phosphate  or  succinate,  etc.,  at  the 
same  hydrogen  ion  concentration  and  the  same  concentration 
of  originally  isoelectric  protein.1 

In  this  way  the  influence  of  ions  on  the  physical  properties  of 
proteins,  especially  in  the  case  of  gelatin,  turned  out  to  be  in 
harmony  with  the  results  of  titration  experiments.  In  the  case  of 
gelatin  and  apparently  also  crystalline  egg  albumin,  only  the 
valency  but  not  the  nature  of  the  ion  in  combination  with  the 
protein  influences  its  properties.  The  statements  to  the  con- 
trary were  due  to  two  errors,  first  and  foremost,  the  failure  to 
measure  the  hydrogen  ion  concentration  of  the  protein  solutions, 
and  second,  the  confusion  of  phenomena  of  solubility  with  phe- 
nomena of  colloidal  behavior. 

5.  THE  AGGREGATION  HYPOTHESIS 

It  was  perhaps  not  very  fortunate  for  the  development  of  a 
theory  of  colloids  that  the  attention  of  investigators  was  focussed 
especially  on  the  phenomena  of  precipitation.  Since  precipita- 
tion is  due  to  an  aggregation  of  particles  it  over-emphasized  the 
significance  of  aggregate  formation.  This  led,  as  we  have  seen, 
to  the  erroneous  idea  that  proteins  do  not  combine  stoichiome- 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  pp.  85,  247,  1920-21. 


16  THEORY  OF  COLLOIDAL  BEHAVIOR 

trically  with  other  compounds,  since  aggregates  were  assumed 
to  react  only  at  their  surface — an  assumption  which,  as  already 
stated,  is  not  warranted  in  the  case  of  proteins,  since  protein  gels 
are  freely  permeable  to  crystalloids.  It  led,  however,  to  another 
equally  fatal  idea,  that  this  aggregate  formation  would  explain 
all  the  colloidal  phenomena.  Thus  when  R.  S.  Lillie1  made  the 
important  observation  that  neutral  salts  depress  the  osmotic 
pressure  of  gelatin  solutions,  it  seemed  natural  to  explain  this 
fact  from  the  precipitating  action  of  salts,  by  assuming  that  the 
addition  of  salt  caused  an  aggregation  of  gelatin  molecules  or  ions 
into  larger  aggregates.  This  would  lead  to  a  diminution  of  the 
number  of  particles  in  solution.  But  it  was  also  found  that  the 
addition  of  salts  depresses  the  viscosity  of  protein  solutions  and 
the  swelling  of  solid  proteins.  We  shall  see  later  that  the 
formation  of  aggregates  out  of  isolated  protein  molecules  or  ions 
increases  the  viscosity  of  a  gelatin  solution.2  Hence,  if  the  addi- 
tion of  a  salt  to  a  protein  solution  diminishes  its  osmotic  pressure 
by  causing  an  increased  formation  of  aggregates  the  same  addi- 
tion of  salt  should  increase  the  viscosity  of  such  a  solution.  The 
reverse,  however,  happens,  the  viscosity  of  the  solution  being 
decreased  by  the  addition  of  salt. 

There  is  nevertheless  a  connection  between  the  phenomena  of 
precipitation  and  the  depressing  effect  of  salts  on  viscosity, 
osmotic  pressure,  and  swelling  of  proteins.  Schulze,  Linder  and 
Picton,  and  Hardy  had  observed  that  in  the  precipitation  of 
colloids  that  ion  is  active  which  has  the  opposite  sign  of  charge 
from  the  protein  particle,  and  that  the  efficiency  of  the  active 
ion  increased  with  its  valency.  The  same  rule  applies  to  the 
depressing  action  of  salts  on  the  osmotic  pressure,  viscosity,  and 
swelling  of  proteins.  By  trying  to  explain  these  latter  effects 
from  the  precipitating  action  of  salts  the  colloid  chemists  put  the 
cart  before  the  horse,  and  were  led  into  a  hopeless  contradiction 
wfth  the  facts.  We  shall  see  that  by  taking  the  reverse  step, 
namely,  of  explaining  the  precipitating  action  of  salts  from  their 
depressing  action  on  osmotic  pressure  and  P.D.  of  protein  solu- 
tions, everything  becomes  clear  and  consistent.  But  this  step 
could  not  be  taken  as  long  as  the  belief  in  the  adsorption  theory 

MILLIE,  R.  S.,  Am.  J.  Physiol.,  vol.  20,  p.  127,  1907-08. 
2LoEB,  J.,  J.  Gen.  Physiol.,  vol.  4,  p.  97,  1921-22. 


HISTORICAL  INTRODUCTION  17 

of  colloids  prevailed.  The  quantitative  explanation  of  the  col- 
loidal behavior  of  proteins  to  be  given  in  this  book  rests  on  the 
proof  that  they  form  true  ionizable  salts  with  acids  and  alkalies. 

6.  PAULI'S  HYDRATION  THEORY 

Laqueur  and  Sackur, l  in  studying  the  influence  of  the  addition 
of  different  quantities  of  NaOH  to  a  given  mass  of  casein, 
assumed  correctly  that  the  two  substances  combined  to  form 
sodium  caseinate.  The  viscosity  of  the  sodium  caseinate  solu- 
tion was  high  and  it  varied  in  a  peculiar  way  with  the  quantity  of 
NaOH  added  to  the  casein.  When  little  NaOH  was  added,  the 
viscosity  increased  at  first  with  an  increase  in  the  quantity  of  the 
NaOH  added  until  a  maximum  was  reached,  when  the  addition  of 
more  NaOH  diminished  the  viscosity  again.  This  again  is  a 
fundamental  fact  which  has  since  been  confirmed  for  the  influ- 
ence of  acids  and  alkalies  not  only  upon  the  viscosity  but  also 
upon  other  properties  of  proteins  and  which  holds  not  only  for 
casein  but  apparently  for  all  proteins. 

Laqueur  and  Sackur  explained  their  results  on  the  basis  of 
Reyher's2  experiments  on  the  viscosity  of  solutions  of  fatty 
acids.  Reyher  had  found  that  the  viscosity  of  solutions  of  salts 
of  the  fatty  acids  is  greater  than  that  of  solutions  of  fatty  acids 
themselves;  and  since  the  salts  of  the  fatty  acids  undergo  elec- 
trolytic dissociation  to  a  much  greater  extent  than  the  acids  it  was 
assumed  that  the  increase  in  viscosity  is  determined  chiefly  by 
the  ionization.  Laqueur  and  Sackur  made  the  same  assumption 
for  the  casein  solutions,  attributing  the  high  viscosity  of  casein 
solutions  to  the  casein  ions,  and  they  support  their  assumption 
by  the  fact  that  the  addition  of  little  NaOH  to  casein  at  first 
increases  the  viscosity  until  a  maximum  is  reached  and  that  the 
addition  of  more  NaOH  diminishes  the  viscosity  again.  A  dimi- 
nution of  viscosity  could  also  be  produced  by  the  addition  of 
neutral  salt  to  the  solution  of  Na  caseinate.  Laqueur  and  Sackur 
assume  that  this  drop  in  the  viscosity  is  caused  by  a  lowering  of 
the  degree  of  electrolytic  dissociation  of  the  Na  caseinate  by  the 
Na  ion  of  the  NaOH  or  NaCl  added  in  excess. 

1  LAQUEUR,  E.  and  SACKUR,  O.,  Beitr.  chem.  Physiol.   u.   PaihoL,  vol.  3, 
p.  193,  1903. 

2  REYHER,  R.,  Z.  physik.  Chem.,  vol.  2,  p.  744,  1888. 


18  THEORY  OF  COLLOIDAL  BEHAVIOR 

The  idea  that  the  viscosity  of  protein  solution  depends  primarily 
upon  the  protein  ion  was  accepted  by  W.  Pauli,1  who  made  the 
additional  hypothesis  that  each  protein  ion  is  hydrated;  i.e., 
that  each  individual  protein  ion  is  surrounded  by  a  considerable 
shell  of  water.  Pauli  worked  with  blood  albumin  which  had 
been  freed  from  salts  by  a  dialysis  continued  for  several  weeks. 
When  he  added  acid  to  water-soluble  albumin,  the  viscosity 
increased  first  from  1.0623  for  the  pure  albumin  solution  to 
1.2937  when  the  concentration  of  HC1  added  to  the  albumin 
solution  was  0.017  N.  When  the  HC1  concentration  was  in- 
creased to  0.05  N  the  viscosity  was  only  1.1667.  The  following 
figures  give  the  data  according  to  Pauli: 

Concentration  of  HC1  0.0  N  0.005  N  0.01  N  0.012  N  0.017  N  0.02  N  0.03  N  0.04  N  0.05  N 
Viscosity 1.06231.2555      1.233     1.274       1.2937     1.27701.2241.18221.1667 

Pauli  assumed  that  the  protein  ions  are  surrounded  by  a  jacket 
of  water,  while  the  non-ionized  molecules  of  protein  he  assumed 
not  to  be  hydrated.  Addition  of  a  little  HC1  to  isoelectric 
albumin  would  cause  the  transformation  of  non-ionized  albumin 
into  albumin  chloride  which  is  highly  ionized  and  hence  assumed 
to  be  highly  hydrated;  the  more  acid  is  added  the  more  albumin 
chloride  and  the  more  hydrated  albumin  ions  should  be  formed. 
Hence,  the  viscosity  should  at  first  increase  with  the  quantity 
of  acid  added,  until  a  point  is  reached  where  the  addition  of  more 
acid  represses  the  degree  of  electrolytic  dissociation  of  the  albu- 
min chloride  on  account  of  the  high  concentration  of  the  Cl  ion 
common  to  both  protein  chloride  and  HC1. 

If  we  intend  to  use  these  ideas  for  the  explanation  of  the  influ- 
ence of  the  valency  of  ions  on  the  physical  properties  of  proteins 
we  are  compelled  to  assume  that  the  degree  of  electrolytic 
dissociation  of  gelatin  salts  with  bivalent  ions  is  lower  than  that 
of  gelatin  salts  with  monovalent  ions.  Since,  e.g.,  the  viscosity 
of  gelatin  chloride  solutions  is  considerably  higher  than  thie 
viscosity  of  gelatin  sulphate  solutions  of  the  same  hydrogen  ion 
concentration  and  the  same  concentration  of  originally  iso- 
electric gelatin,  we  should  have  to  conclude  that  the  degree  of 
electrolytic  dissociation  of  gelatin  sulphate  is  considerably  less 
than  that  of  gelatin  chloride. 

1  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912;  "Kol- 
loidchemie  der  Eiweisskorper,"  Dresden  and  Leipsic,  1920. 


HISTORICAL  INTRODUCTION  19 

The  writer  put  this  theory  to  a  test  by  measuring  the  electrical 
conductivity  of  solutions  of  different  gelatin  salts  at  different  pH, 
with  the  result  that  the  parallelism  between  the  concentration  of 
protein  ions  and  the  physical  properties  of  proteins  demanded 
by  Pauli's  theory  could  not  be  demonstrated  (see  Chap.  VII). 
Lorenz,1  Born,2  and  other  authors  have  recently  reached  the 
conclusion  that  the  idea  of  a  hydration  of  ions  is  not  tenable  in 
the  case  of  polyatomic  ions.3 

The  increase  in  viscosity  of  certain  protein  solutions  through 
the  addition  of  acid  or  alkali  to  isoelectric  proteins  is  caused 
by  the  ionization  of  proteins,  but  the  connection  is  not  the  di- 
rect one  suggested  by  Laqueur  and  Sackur  but  an  indirect  one 
due  to  the  role  of  protein  ions  in  the  establishment  of  a  Donnan 
equilibrium. 

7.  DONNAN'S  MEMBRANE  EQUILIBRIUM 

With  the  proof  of  the  stoichiometrical  character  of  the  com- 
bination of  proteins  with  acids  and  alkalies  the  explanation  of 
colloidal  behavior  on  the  basis  of  the  adsorption  theory  became 
untenable  and  another  theoretical  basis  had  to  be  found.  The 
explanation  offered  in  this  volume  is  based  on  Donnan's  theory 
of  membrane  equilibria. 

Donnan4  has  shown  that  when  a  membrane  separates  two 
solutions  of  electrolytes  one  of  which  contains  one  ion  which 
cannot  diffuse  through  the  membrane  while  all  the  other  ions 
can  diffuse  through  the  membrane,  the  result  will  be  an  unequal 
distribution  of  the  diffusible  ions  on  the  opposite  sides  of  the 
membrane.  At  equilibrium  the  products  of  the  concentrations 
of  each  pair  of  oppositely  charged  diffusible  ions  are  the  same  on 
the  opposite  sides  of  the  membrane.  This  unequal  concentration 
of  the  crystalloidal  ions  must  give  rise  to  potential  differences 

1  LORENZ,  R.,  Z.  Elektrochem.,  vol.  26,  p.  424,  1920. 

2  BORN,  M.,  Z.  Elektrochem.,  vol.  26,  p.  401,  1920. 

3  The  term  "hydration"  is  often  used  in  colloid  chemistry  in  a  vague 
way  to  designate  such  phenomena  as  the  swelling  of  proteins  which  is  a 
purely  osmotic  phenomenon.     It  is  obvious  that  it  can  only  lead  to  confusion 
if  the  term  hydration  is  used  for  osmotic  pressure.     In  this  volume  the  term 
hydration  is  only  used  in  the  sense  of  Kohlrausch  and  Pauli. 

4  DONNAN,  F.  G.,  Z.  Elektrochem.,  vol.  17,  p.  572,  1911. 


20 


THEORY  OF  COLLOIDAL  BEHAVIOR 


and  osmotic  forces,  and  we  intend  to  show  that  these  forces 
furnish  the  explanation  of  colloidal  behavior. 

It  may  be  best  to  quote  Donnan's  theory  in  his  own  words : 

"We  suppose  that  the  membrane  (indicated  in  the  following  diagram 
by  a  vertical  line)  be  impermeable  for  the  anion  R  of  a  salt  NaR  (and 
also  for  the  non-dissociated  part  of  the  salt  NaR),  but  permeable  for  all 
the  other  ions  and  salts  to  be  considered  in  this  connection  .  .  . 

"Suppose  that  in  the  beginning  we  have  a  solution  of  NaR  on  one  side 
of  the  membrane  (indicated  by  a  vertical  line)  and  of  NaCl  on  the  other 
side 


Na 

R 

(1) 


Na 
Cl 


In  this  case  NaCl  will  diffuse  from  (2)  to  (1).     In  the  end  the  following 
equilibrium  will  result: 


Na 

R 

Cl 

(1) 


Na 


Cl 

(2) 


"When  this  equilibrium  is  established  the  energy  required  to  transport 

+ 

reversibly  and  iso thermally  1  grammolecule  Na  from  (2)  to  (1)  equals 
the  energy  which  can  be  gained  by  the  corresponding  reversible  and 

isothermal  transport  of  a  grammolecule  Cl.  In  other  words,  we  con- 
sider the  following  infinitely  small  isothermal  and  reversible  change  of 
the  system: 


SnMolNa  (2)  ->  (1) 


UnMolCl    (2)  -»  (1)  J 

"The  energy  which  can  be  gained  in  this  way  (i.e.,  the  diminution  of 
free  energy)  is  zero,  hence: 


log 


log  --2  =  0 


or 


[Nak[Cl]2  =  [Nh-lCl]! 
where  the  brackets  signify  molar  concentrations." 


(1) 


HISTORICAL  INTRODUCTION  21 

This  last  equation  is  the  equilibrium  equation  which  states 
that  the  product  of  the  concentrations  of  a  pair  of  diffusible 
cations  and  anions  on  one  side  of  the  membrane  is  equal  to  the 
product  of  the  concentrations  of  the  same  pair  of  diffusible  anions 
and  cations  on  the  other  side.  Since  on  the  side  of  the  non- 
diffusible  (protein)  anion  the  concentration  of  cations  Na  is  the 
sum  of  the  cations  in  combination  with  the  non-diffusible  anion 
plus  the  cations  in  combination  with  the  Cl,  while  on  the  other 
side  of  the  membrane  the  concentration  of  the  Na  ions  is  only  that 
of  Na  in  combination  with  Cl  and  equal  to  the  concentration  of 
Cl,  it  is  obvious  that  Donnan's  equation  (1)  can  only  be  fulfilled 
if 

[Na]1>[Na]2 
and 


This  inequality  of  concentration  of  the  diffusible  ions  on  the 
opposite  sides  of  the  membrane  accounts,  as  we  shall  see,  for  the 
influence  of  electrolytes  on  all  those  properties  which  colloid 
chemistry  has  vainly  tried  to  explain  on  the  basis  of  the  disper- 
sion and  hydration  hypotheses.  The  reader  will  notice  that  the 
essential  condition  determining  the  equilibrium  is  the  existence 
of  two  phases  separated  by  a  membrane,  one  phase  containing 
an  ion  which  cannot  diffuse  through  a  membrane  which  is  easily 
permeable  for  all  the  other  ions. 

This  difference  in  the  concentration  of  the  diffusible  ions  on 
opposite  sides  of  the  membrane  must  lead  to  potential  differences 
on  opposite  sides  of  the  membrane  and  Donnan  shows  that  this 
difference  must  be  (on  the  basis  of  Nernst's  well-known  formula) 

RT,      [Na]2      RT,      [Cl]i 
TI  -  7T2  =         log  l—  ^  =  -=-  log  l-^- 

[Na]x  [Cl], 

•prp 

or  since  -^r  =  58  millivolts  (at  room  temperature)  the  potential 
r 

difference  on  opposite  sides  of  the  membrane  should  be  in  millivolts 

Tl_T2=581og[4^  =  581og^ 
[Na],  [Cl], 


22  THEORY  OF  COLLOIDAL  BEHAVIOR 

The  writer  has  tested  this  consequence  of  Donnan's  theory 
for  solutions  of  protein  salts  separated  from  water  by  a  collodion 
membrane,  with  the  result  that  the  theory  was  completely 
confirmed.  Through  these  measurements  of  the  membrane 
potentials  the  correctness  of  Donnan's  theory  was  proved  beyond 
doubt. 

It  may  be  pointed  out  that  it  is  not  necessary  that  the  non- 
diffusible  ion  be  a  colloid;  it  is  only  necessary  that  there  be  a 
membrane  which  prevents  one  ion  from  diffusing;  it  is  immaterial 
whether  or  not  this  latter  ion  be  a  crystalloid  or  a  colloid.  If  we 
had  a  membrane  impermeable  for  a  SO4  ion  but  permeable  for 
Na  and  Cl  ions,  solutions  of  NaCl  and  Na2SO4  separated  by  the 
membrane  would  give  rise  to  the  Donnan  equilibrium,  and  the 
Na2SO4  solution  would  probably  resemble  a  solution  of  Na  pro- 
teinate  in  regard  to  certain  features  of  colloidal  behavior,  e.g., 
osmotic  pressure  and  P.D.  against  water. 

Donnan  and  his  collaborators  proved  the  existence  of  the 
inequality  of  the  concentration  of  the  diffusible  ions  of  two  salt 
solutions  on  the  opposite  sides  of  a  membrane  when  one  of  the 
ions  was  not  able  to  diffuse  through  the  membrane.  Thus 
Donnan  and  Allmand  investigated 

"the  distribution  of  potassium  chloride  between  two  compartments 
separated  by  a  copper  ferrocyanide  diaphragm,  one  compartment  of 
which  contained  potassium  ferrocyanide  (the  membrane  being  imper- 
meable to  the  Fe(CN)6  ion).  The  higher  concentration  of  potassium 
chloride  on  the  side  free  from  potassium  ferrocyanide,  and  the  relation 
of  this  unequal  distribution  to  the  concentration  of  the  chloride  and 
ferrocyanide,  were  experimentally  established.  The  results  obtained 
agreed,  in  general,  with  the  view  of  membrane  equilibria  proposed 
by  Donnan,  but  a  discussion  of  the  distribution  data  combined  with 
electromotive-force  measurements  appeared  to  show  that,  at  all  events 
in  the  case  of  a  copper  ferrocyanide  membrane  and  potassium  ferrocy- 
anide solutions,  the  phenomena  are  not  so  simple  as  supposed  in  the 
theory."1 

More  recently  Donnan  and  Garner2  investigated  the  equilib- 
rium concentration  of  solutions  of  Na  and  K  ferrocyanides  and 
of  Na  and  Ca  ferrocyanides  across  a  copper  ferrocyanide  mem- 

1  DONNAN,  F.  G.  and  ALLMAND,  A.  J.,  J.  Chem.  Soc.,  vol.  105,  p.  1963, 
1914. 

2  DONNAN,  F.  G.  and  GARNER,  W.  E.,  J.  Chem.  Soc.,  vol.  115,  p.  1313,  1919. 


HISTORICAL  INTRODUCTION  23 

brane,  and  the  results  were  in  general  agreement  with  Donnan's 
theory.  They  also  investigated  a  liquid  membrane,  namely,  amyl 
alcohol,  and  the  electrolytes  employed  were  KC1  and  LiCl. 

."So  far  as  the  preliminary  experiments  go,  the  equilibrium  concentra- 
tion of  the  Li  and  Cl  ions  and  the  undissociated  part  of  the  electrolyte 
agree  with  Donnan's  theory." 

We  shall  see  that  Donnan's  theory  explains  the  influence  of 
electrolytes  on  the  physical  properties  of  proteins.  He  foresaw 
the  bearing  which  his  theory  was  likely  to  have  for  colloid  chem- 
istry and  physiology,  as  is  shown  by  the  following  remarks. 

"In  this  paper  an  attempt  is  made  to  describe  ion  equilibria  which 
are  bound  to  occur  when  certain  ions  (or  their  corresponding  non- 
dissociated  salt)  cannot  diffuse  through  a  membrane.  Such  equilibria 
possess  a  great  importance  for  the  theory  of  dialysis  and  of  colloids 
as  well  as  for  the  mechanism  of  the  cell  and  for  general  physiology." 

As  far  as  the  writer  is  aware,  Procter  and  J.  A.  Wilson  were  the 
only  authors  who  attempted  the  application  of  Donnan's  theory 
to  colloidal  problems. 

Procter1  proposed  in  1914  an  ingenious  theory  of  swelling 
based  on  Donnan's  membrane  equilibrium.  According  to  this 
theory  the  force  which  causes  the  entrance  of  water  into  the  gel 
and  thus  determines  the  swelling  is  the  osmotic  pressure  of  the 
excess  of  crystalloidal  ions  inside  over  that  outside  the  gel,  this 
excess  being  caused  by  the  Donnan  equilibrium.  The  opposing 
force  which  limits  the  swelling  is  the  force  of  cohesion  of  the 
colloidal  particles. 

According  to  Procter,  the  gelatin  ion  constituting  a  jelly  of 
gelatin  chloride  cannot  diffuse  and  hence  can  exercise  no  osmotic 
pressure,  while  the  chlorine  'anions  in  'combination  with  them  are 
retained  in  the  jelly  by  the  electrostatic  attraction  of  the  gelatin 
ion,  but  exert  osmotic  pressure.  This  difference  in  the  diffusi- 
bility  of  the  two  opposite  ions  of  gelatin  chloride  gives  rise  to  the 
establishment  of  Donnan's  membrane  equilibrium. 

Procter  put  solid  gelatin  chloride  into  a  watery  solution  of 
HC1  and  determined  by  titration  the  distribution  of  free  HC1 
inside  tlie  gel  and  outside  at  the  time  of  equilibrium.  In  this 
case  there  exists  inside  the  gel  free  HC1  and  gelatin  chloride,  out- 

1  PROCTER,  H.  R.,  J.  Chem.  Soc.,  vol.  105,  p.  313,  1914.  PROCTER,  H.  R. 
and  WILSON,  J,  A.,  J,  Chem,  Soc.,  vol.  109,  p.  307,  1916. 


24  THEORY  OF  COLLOIDAL  BEHAVIOR 

side  HC1.  The  relative  concentration  of  free  HC1  inside  and  out- 
side at  the  time  of  equilibrium  is  determined  by  the  equation  for 
the  Donnan  equilibrium 

x2  =  y  (y  +  z)  (1) 

where  x  is  the  concentration  of  the  H  and  Cl  ions  in  the  outside 
solution,  y  the  concentration  of  H  and  Cl  ions  of  the  free  HC1 
inside  the  gel,  and  z  the  concentration  of  Cl  ions  in  combination 
with  the  gelatin  cation,  x  and  y  can  be "  determined  experi- 
mentally and  z  can  be  calculated  with  the  aid  of  the  equation. 
In  other  words,  the  distribution  of  the  H  and  Cl  ions  on  the 
opposite  sides  of  a  membrane  is  such  that  the  product  of  the 
concentrations  of  the  pair  of  oppositely  charged  ions  is  equal  in 
both  phases. 

"The  gelatin  salt,  like  other  salts,  is  highly  ionised  into  the  anion  and 
a  colloid  cation,  which  either  from  polymerisation  or  other  causes 
peculiar  to  the  colloid  state  cannot  diffuse  and  exerts  no  measurable 
osmotic  pressure,  whilst  its  anion  is  retained  in  the  jelly  by  electro- 
chemical attraction  of  the  colloid  ion,  but  exerts  osmotic  pressure  which, 
on  the  one  hand,  causes  the  mass  to  swell  with  absorption  of  the  external 
solution,  and,  on  the  other,  expels  a  portion  of  the  acid,  both  anion 
and  hydrion,  from  this  solution  absorbed,  the  result  in  equilibrium  being 
that  the  jelly  is  poorer  in  hydrion  and  more  concentrated  in  anion  than 
the  external  acid  solution,  the  difference  of  concentration  between 
anion  and  hydrion  in  the  jelly  being,  of  course,  equal  to  the  ionised 
anion  of  the  gelatin  salt,  and  electrically  balanced  by  the  positive 
gelatin  ions;  whilst  the  hydrion  concentration  in  the  jelly  is  less  than 
that  of  the  outer  solution  by  the  amount  of  acid  expelled."1 

By  establishing  a  connection  between  the  volume  of  the  gel 
and  the  observed  values  of  x  and  y,  Procter  and  Wilson  were  able 
to  calculate  the  effect  of  different  concentrations  of  HC1  on  the 
swelling  of  gelatin,  and  they  could  show  why  little  acid  increased 
the  swelling  until  a  maximum  was  reached  and  why  the  addition 
of  more  acid  depressed  the  swelling.  They  could  further  show  why 
the  addition  of  neutral  salt  caused  a  depression  of  the  swelling. 

It  is  of  interest  to  inquire  why  this  theory  of  swelling  was  not 
accepted  and  only  rarely  mentioned  in  the  colloidal  literature. 

1  PROCTER,  H,  R.  and  WILSON,  J.  A.,  J,  Chem.  Soc.,  vol.,  109,  pp.  309-310, 
1916. 


HISTORICAL  INTRODUCTION  25 

In  the  first  place,  the  application  of  Donnan's  theory  to  the 
behavior  of  proteins  requires  the  proof  that  proteins  form  true 
salts  with  acids  and  alkalies  and  that  these  salts  dissociate 
electrolytically  into  a  protein  ion  and  a  crystalloidal  cation  or 
anion.  Such  an  assumption  was  in  conflict  with  the  adsorption 
hypothesis  accepted  by  the  colloid  chemists.  Moreover,  the 
application  of  the  Donnan  theory  to  proteins  tacitly  implied 
that  only  the  valency  and  sign  of  charge  should  have  an  effect 
on  the  proteins,  while  the  nature  of  the  ion  should  have  no 
effect;  and  this  was  in  conflict  with  the  belief  in  the  Hofmeister 
ion  series.  But  even  authors,  like  Robertson,  who  was  a  cham- 
pion of  the  purely  chemical  conception  of  the  behavior  of  proteins, 
refused  to  accept  Procter's  theory  of  swelling. 

"  There  should  be  a  measurable  potential  difference  between  the 
gelatin  jelly  and  the  external  medium.  This  potential  difference  has 
been  sought  for  by  Ehrenberg  who  was  unable  to  detect  any  measurable 
potential  between  the  interior  of  a  jelly  and  the  external  medium."1 

This  gap  has  been  filled  by  the  writer's  experiments,  which 
have  demonstrated  the  existence  of  this  potential.  The  writer 
has  not  only  been  able  to  furnish  support  for  Procter's  theory 
of  swelling  but  has  also  been  able  to  show  that  the  potential 
differences  across  a  membrane  separating  a  solution  of  a  protein 
salt  from  pure  water  fully  support  Donnan's  theory.2  When  we 
have  a  solution  of  a  gelatin-acid  salt  with  monovalent  anion, 
e.g.,  gelatin  chloride  (or  gelatin  phosphate)  inside  a  collodion  bag 
which  is  dipped  into  pure  water,  the  hydrogen  ion  concentration 
as  well  as  the  anion  concentration  on  the  opposite  sides  of  the 
membrane  are  different  when  osmotic  equilibrium  is  established. 
The  writer  was  able  to  show  that  the  potential  differences  calcu- 
lated from  this  difference  of  the  concentration  of  ions  on  the 
basis  of  Nernst's  formula  agree  with  the  actually  observed  P.D., 
and  that  the  calculated  P.D.  is  the  same  whether  based  on  a 
measurement  of  the  difference  in  the  concentration  of  the  hydro- 
gen ions  or  of  the  difference  in  the  concentration  of  the  chlorine 
ions  on  the  opposite  sides  of  the  membrane.  This  latter  fact 

1  ROBERTSON,  T.  B.,  "The  Physical  Chemistry  of  the  Proteins,"  p.  297, 
New  York,  London,  Bombay,  Calcutta,  and  Madras,  1918. 
2LoEB,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  667,  1920-21. 


26  THEORY  OF  COLLOIDAL  BEHAVIOR 

seems  a  complete  proof  for  the  correctness  of  Donnan's  theory  of 
membrane  equilibrium,  and  also  a  further  proof  for  the  correctness 
of  the  purely  chemical  conception  of  the  combination  of  proteins 
with  acids  and  alkalies.  For  unless  the  proteins  form  true  ioniz- 
able  salts  with  acids  and  alkalies  they  cannot  fulfill  the  require- 
ments of  the  Donnan  equilibrium. 

It  was,  however,  possible  to  go  a  step  further,  inasmuch  as 
these  membrane  potentials  showed  the  typical  colloidal  charac- 
teristics noticed  in  connection  with  viscosity,  swelling,  and 
osmotic  pressure,  namely,  the  potential  difference  across  the  mem- 
brane was  depressed  by  the  addition  of  neutral  salts,  was  increased 
by  the  addition  of  little  acid  to  isoelectric  protein,  and  depressed 
by  the  addition  of  more  acid;  the  depressing  effect  was  in  both 
cases  due  to  the  ion  with  the  opposite  sign  of  charge  to  that  of  the 
protein  ion,  and  finally  the  depressing  influence  increased  rapidly 
with  the  valency  of  the  active  ion — while  the  other  characteristics 
of  the  ion  aside  from  sign  and  valency  had  no  effect.  In  this 
case  there  was  not  the  slightest  doubt  that  the  effects  were  exclu- 
sively the  result  of  the  Donnan  equilibrium  since  they  could  be 
mathematically  predicted  and  calculated  from  the  equilibrium 
formula. 

The  writer  was  able  to  show,  in  addition,  that  the  analogous 
behavior  of  the  osmotic  pressure  and  viscosity  of  protein  solutions 
could  be  explained  and  calculated  on  the  basis  of  Donnan's 
theory. 

It,  therefore,  turns  out  that  two  laws  of  classical  chemistry 
suffice  to  explain  colloidal  behavior  quantitatively  and  mathe- 
matically, and  these  two  laws  are  the  stoichiometrical  law  and 
Donnan's  theory  of  membrane  equilibria.  The  proof  for  this 
statement  is  the  purpose  of  this  volume. 


CHAPTER  II 

QUALITATIVE   PROOF    OF    THE  CORRECTNESS  OF 
THE  CHEMICAL  VIEWPOINT 

PREPARATION  OF  PROTEINS  FREE  FROM  IONOGENIC  IMPURITIES 

The  first  problem  confronting  the  chemist  is  to  find  a  method 
which  permits  him  to  settle  definitely  the  problem  whether  only 
one  or  both  ions  of  a  salt  combine  with  a  protein.  This  decision 
was  not  possible  with  the  old  methods.  Those  who  believe  in 
the  adsorption  theory  assume  that  both  ions  of  a  salt  are  adsorbed 
by  colloids  and  Pauli  holds  that  both  ions  of  a  salt  are  adsorbed  by 
the  non-ionized  molecules  of  protein.1 

When  a  block  of  gelatin  is  put  into  a  salt  solution,  the  solution 
enters  into  the  interstices  between  the  gelatin  molecules  constitut- 
ing the  block.  When  such  a  block  of  gelatin  is  melted,  of  course, 
both  ions  of  the  salt  are  found,  but  nobody  can  tell  whether  the  salt 
found  was  only  the  salt  contained  in  the  interstices  of  the  original 
gel  or  whether  it  was  in  combination  with  the  gelatin.  This  diffi- 
culty can  be  circumvented  by  using  solid  gelatin  in  the  form  of  a 
very  fine  powder  of  grains  approximately  equal  in  size.  When 
such  powdered  gelatin  is  exposed  to  a  salt  solution  for  some  time, 
we  can  ascertain  with  certainty  by  a  process  of  washing  whether 
one  or  both  ions  are  in  combination  with  the  gelatin.  After 
a  small  mass  of  the  powdered  gelatin  has  been  exposed  to  a 
salt  solution  for  about  1  hour,  it  is  put  on  a  filter  and  perfused, 
with  stirring,  about  six  times  or  more  with  25  c.c.  of  ice-cold 
distilled  water.  The  water  must  be  cold  since  otherwise  the 
granules  will  coalesce,  rendering  the  process  of  washing  futile. 
By  this  procedure  it  is  possible  to  remove  the  salt  solution 
between  the  granules  of  gelatin,  without  removing  the  ions  in 
chemical  combination  with  the  gelatin — at  least  not  by  the  six 
washings.  By  using  this  method  of  washing  we  can  ascertain 

1  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912. 

27 


28  THEORY  OF  COLLOIDAL  BEHAVIOR 

whether  both  or  only  one  of  the  two  oppositely  charged  ions  of  a 
salt  enters  into  combination  with  gelatin. 

Such  experiments  show  that  at  a  given  hydrogen  ion  concentra- 
tion either  the  cation  or  only  the  anion  or  neither  ion  can  combine 
with  a  protein;  and  that  it  depends  solely  on  the  hydrogen  ion 
concentration  of  the  solution  which  of  the  three  possibilities  exists.1 

Proteins  are  amphoteric  electrolytes  which  exist  in  three  states, 
according  to  their  hydrogen  ion  concentration,  namely,  (a)  as 
non-ionogenic  or  isoelectric  protein;  (6)  metal  proteinate  (e.g., 
Na  or  Ca  proteinate);  and  (c)  protein-acid  salts  (e.g.,  protein 
chloride,  protein  sulphate,  etc.).  We  will  use  gelatin  as  an  illus- 
tration. At  one  definite  hydrogen  ion  concentration,  namely, 
that  of  the  isoelectric  point,  which  in  the  case  of  gelatin  lies  at 
10~4-7N  (or  in  S^rensen's  logarithmic  symbol  at  pH  =  4.7),  gelatin 
can  combine  practically  with  neither  anion  nor  cation  of  an  elec- 
trolyte. At  a  pH>4.7,  gelatin  can  combine  only  with  cations 
(forming  metal  gelatinate,  e.g.,  Na  gelatinate);  at  a  pH<4.7, 
gelatin  combines  with  anions  (forming  gelatin  chloride,  etc.). 
This  was  proved  in  the  following  way:  Doses  of  1  gm.  of  finely 
powdered  commercial  gelatin  (going  through  sieve  60  but  not 
through  80),  which  happened  to  have  a  pH  of  7.0,  were  brought  to 
different  hydrogen  ion  concentrations  by  putting  them  for  1  hour 
at  about  15°C.  into  100  c.c.  of  HNO3  solutions  varying  in  concen- 
tration from  M/8,192  to  M/8.  Owing  to  the  Donnan  equilib- 
rium the  hydrogen  ion  concentration  inside  a  gelatin  granule  is 
lower  than  that  outside.  After  this,  each  dose  of  1  gm.  of  gelatin 
was  put  on  a  filter,  the  acid  being  allowed  to  drain  off,  and  each 
dose  was  washed  once  or  twice  with  25  c.c.  of  cold  water  (at  5°C. 
or  less)  to  remove  the  greater  part  of  the  acid  between  the 
granules  of  the  powdered  gelatin.  These  different  doses  of 
originally  1  gm.  of  gelatin,  each  of  which  now  possessed  a  different 
pH,  were  put  for  1  hour  each  into  a  separate  beaker  containing 
the  same  concentration,  e.g.,  M/64,  of  silver  nitrate  at  a  temper- 
ature of  15°C.  Each  dose  of  powdered  gelatin  was  then  put  on  a 
filter  and  washed  with  stirring  six  or  eight  times  each  with  25  c.c. 
of  ice-cold  water.  This  washing  serves  the  purpose  of  removing 
the  AgNO3  held  in  solution  between  the  granules,  thus  allowing 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  1,  pp.  39,  237,  1918-19.     Science,  vol. 
52,  p.  449,  1920.     /.  chim.  physique,  vol.  18,  p.  283,  1920. 


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CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          29 

us  to  ascertain  where  the  Ag  is  in  combination  with  gelatin  and 
where  it  is  not  in  combination,  since  the  Ag  not  in  combination 
with  gelatin  can  be  removed  by  the  washing  while  the  former  can- 
not, or  at  least  only  extremely  slowly  (by  altering  the  pH). 
After  having  removed  the  AgN03  not  in  combination  with  gelatin 
by  washing  with  cold  water,  the  gelatin  is  melted  by  heating 
to  40°C.,  enough  distilled  water  is  added  to  bring  the  volume  of 
each  gelatin  solution  to  100  c.c.,  the  pH  of  a  sample  of  each  solu- 
tion is  determined  potentiometrically,  and  the  solutions  are 
exposed  in  test-tubes  to  light,  the  previous  manipulations  having 
been  carried  out  in  a  dark  room  (with  the  exception  of  the  deter- 
mination of  pH,  for  which  only  part  of  the  gelatin  solution  was 
used).  In  20  minutes  all  the  gelatin  solutions  with  a  pH>4.7, 
i.e.,  from  pH  4.8  and  above,  upon  exposure  to  strong  light  become 
opaque  and  then  brown  or  black,  while  all  the  solutions  of  pH  < 
4.7,  i.e.,  from  4.6  and  below,  remain  transparent  even  when 
exposed  to  light  for  months  or  years  (Fig.  1).  The  solutions  of 
pH  =  4.7  become  opaque,  but  remain  white,  no  matter  how  long 
they  may  have  been  exposed  to  light.  At  this  pH — the  isoelectric 
point — gelatin  is  not  in  combination  with  Ag,  but  it  is  sparingly 
soluble.  Hence,  the  cation  Ag  is  only  in  chemical  combination 
with  gelatin  when  the  pH  is  >4.7.  At  pH  4.7  or  below  gelatin 
is  not  able  to  combine  with  Ag  ionogenically.  This  statement 
was  confirmed  by  volumetric  analysis. 

The  same  tests  can  be  made  for  any  other  cation  the  presence 
of  which  can  be  easily  demonstrated.  Thus,  when  powdered 
gelatin  of  different  pH  is  treated  with  NiCl2,  and  the  NiCl2  not 
in  combination  with  gelatin  be  removed  by  washing  with  cold 
water,  the  presence  of  Ni  can  be  demonstrated  in  all  gelatin 
solutions  with  a  pH  >4.7  by  using  dimethylglyoxime  as  an  indi- 
cator. All  gelatin  solutions  of  pH  of  4.8  or  above  assume  a 
crimson  color  upon  the  addition  of  dimethylglyoxime,  while  all 
the  others  remain  colorless.  If  we  use  copper  instead  of  Ag  or 
Ni  as  a  cation,  treating  gelatin  with  copper  acetate,  and  washing 
afterwards,  the  gelatin  is  blue  and  opaque  when  its  pH  is  4.8  or 
above,  but  is  colorless  and  clear  for  pH<4.7.  Most  striking  are 
the  results  with  basic  dyes,  e.g.,  basic  fuchsin  or  neutral  red,  after 
sufficient  washing  with  cold  water;  only  those  gelatin  solutions 
are  red  whose  pH  is  above  4.7,  while  the  others  are  colorless. 


30  THEORY  OF  COLLOIDAL  BEHAVIOR 

On  the  acid  side  of  the  isoelectric  point,  i.e.,  at  pH<4.7,  the 
gelatin  is  in  combination  with  the  anion  of  the  salt  used.  This 
can  be  demonstrated  in  the  same  way  by  bringing  different  doses 
of  powdered  gelatin  to  different  pH  and  treating  them  for  1  hour 
with  a  dilute  solution  of  a  salt  whose  anion  easily  betrays  itself, 
e.g.,  M/128  K4Fe(CN)6.  If  after  this  treatment  the  powdered 
gelatin  is  washed  six  times  or  oftener  with  cold  water  to  remove 
the  Fe(CN)6  not  in  chemical  combination  with  gelatin  and  if  1 
per  cent  solutions  of  these  different  samples  of  gelatin  are  made, 
it  is  found  that  when  the  pH  is  <4.7  the  gelatin  solution  turns 
blue  after  a  few  days  (due  to  the  formation  of  ferric  salt),  while 
solutions  of  gelatin  with  a  pH  of  4.7  or  above  remain  permanently 
colorless  (Fig.  2).  Hence,  gelatin  enters  into  chemical  combina- 
tion with  the  anion  Fe(CN)6  only  when  pH  is  <4.7.  The  same 
fact  can  be  demonstrated  through  the  addition  of  ferric  salt  when 
gelatin  has  been  treated  with  NaCNS,  the  anion  CNS  being  in 
combination  with  gelatin  only  where  the  pH  is  <4.7.  Acid  dyes, 
like  acid  fuchsin,  combine  with  gelatin  only  when  the  pH  is 
<4.7.x 

In  this  way  it  can  be  shown  that  when  the  pH  is  >4.7  gelatin 
can  combine  only  with  cations;  when  the  pH  is  <4.7  gelatin  can 
combine  only  with  anions,  while  at  pH  4.7  (the  isoelectric  point) 
gelatin  can  combine  with  neither  anion  nor  cation.  The  idea 
that  both  ions  are  adsorbed  or  combine  with  a  protein  simultane- 
ously is  no  longer  tenable,  since  otherwise  both  ions  of  the  salt 
should  have  been  discovered  on  both  sides  of  the  isoelectric  point. 

It  follows  also  that  a  protein  solution  is  not  adequately  defined 
by  its  concentration  of  protein  but  that  the  hydrogen  ion  con- 
centration must  also  be  known,  since  each  protein  occurs  in  three 
different  forms — possibly  isomers — according  to  its  hydrogen 
ion  concentration. 

Let  us  now  return  once  more  to  the  experiment  in  which  doses 
of  powdered  gelatin  were  brought  to  a  different  pH  and  subse- 

1  In  these  experiments  it  may  happen  that  a  few  individual  granules  do 
not  give  off  their  stain  at  the  isoelectric  point  or  on  the  alkaline  side  of  the 
isoelectric  point,  due  probably  to  experimental  shortcomings.  When  the 
gelatin  is  melted  the  solution  may  show  an  indication  of  red.  The  difference 
between  the  gelatin  on  the  alkaline  and  on  the  acid  side  is,  however, 
sufficiently  striking  even  if  this  slight  error  interferes. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT  31 

quently  treated  for  1  hour  with  the  same  concentration  of  AgNO3, 
e.g.,  M/64  AgNO3,  and  then  washed.  In  this  case,  the  exposure 
to  light  showed  us  that  silver  gelatinate  existed  only  on  the  alka- 
line side  of  the  isoelectric  point,  since  only  on  that  side  did  the 
gelatin  turn  black.  When  we  now  add  enough  alkali  to  the 
gelatin  solutions  with  a  pH  of  4.6  or  less  to  bring  their  pH  to  4.8 
or  above,  they  will  not  turn  black  when  exposed  to  light.  This 
shows  that  the  gelatin  of  pH  below  4.6  did  not  contain  any 
demonstrable  quantity  of  silver.1  It  was  conceivable  that  such 
gelatin  of  pH  below  4.6  contained  Ag  in  a  non-ionogenic  form.  If 
this  were  the  case,  this  fact  should  have  betrayed  itself  in  a 
blackening  upon  the  addition  of  enough  alkali  to  bring  the  pH 
above  4.7. 

When  we  bring  powdered  gelatin  of  pH>4.7,  which  has  been 
treated  with  M/64  AgNO3  and  washed,  to  a  pH  of  4.7,  or  below, 
the  silver  which  was  in  combination  with  the  gelatin  can  be 
removed  by  washing  with  cold  water,  and  such  gelatin  will  not 
turn  black  when  subsequently  exposed  to  light,  provided  the 
washing  had  been  adequate. 

When  we  include  that  part  of  the  gelatin  molecule  which 
cannot  react  with  other  electrolytes  in  brackets,  while  the  part 
of  the  molecule  which  is  capable  of  reacting  with  other  electro- 
lytes is  kept  outside  the  brackets,  we  can  symbolize  our  results 
in  the  following  way  : 

Isoelectric  gelatin  is  entirely  inside  the  brackets  since  at  the 
isoelectric  point  gelatin  can  combine  neither  with  anions  nor  with 
cations, 


-NH2  1 

—  COOHj 


On  the  alkaline  side  from  the  isoelectric  point  practically  only 
COOH  groups  of  the  molecule  are  capable  of  reacting  with 
other  compounds  and  we  represent  the  protein  molecule  on  this 
side  in  the  following  form: 

1  This  dogmatic  presentation  of  our  results  is  only  approximately  correct, 
since  a  trace  of  anion  should  also  combine,  theoretically  at  least,  on  the 
alkaline  side  of  the  isoelectric  point;  and  a  trace  of  cation  on  the  acid  side, 
at  least  near  the  isoelectric  point.  As  a  matter  of  fact,  however,  this  cannot 
be  demonstrated,  though  the  theory  of  amphoteric  electrolytes  demands 
that  this  should  be  so. 


32  THEORY  OF  COLLOIDAL  BEHAVIOR 


[R 


-NH; 


— COOH 

Such  proteins  behave  as  if  they  were  simple  (probably  polybasic) 
fatty  acids,  the  rest  of  the  molecule  not  participating  in  the  reac- 
tion. In  the  presence  of  a  hydroxide,  e.g.,  NaOH,  sodium  pro- 
teinate  is  formed 


—  NH 


.—  COOH  +  NaOH    "   |_1X—  COONa  +  H2O 
and   the   sodium    proteinate   dissociates   electrolytically  into  a 
protein  anion  and  a  Na  ion 


-  COONa       L A  "—  COO  +  Na" 

When  other  electrolytes  are  present  they  can  of  course  exchange 
their  cation  with  the  Na  of  the  protein  salt.  Our  symbol  con- 
siders only  one  COOH  group,  but  it  is  probable  that  as  a  rule 
more  than  one  COOH  group  of  a  protein  molecule  combines 
with  alkali  (Bugarszky  and  Liebermann,  Sackur,  Robertson, 
S^rensen,  Pauli,  Northrop1). 

On  the  acid  side  of  the  isoelectric  point  only  the  NH2  groups  of 
the  molecule  are  capable  of  reacting  with  other  compounds  and 
we  represent  the  protein  molecule  on  this  side  in  the  following 
form: 


[R 


_NH2 


COOH 


In  this  form  the  proteins  behave  like  NH3  which  according  to 
Werner2  is  capable  of  adding  an  acid,  e.g.,  HC1,  the  H  ion  of  the 
acid  being  added  directly  to  the  N  while  the  Cl  remains  outside 

H 

the  ring  of  the  4H  in  the  following  way:  HNHC1.     It  has  been 

H 

1  NORTHROP,  J.  H.,  /.  Gen.  PhysioL,  vol.  3,  p.  715,  1920-21. 

2  WERNER,  A.,  "  Neuere  Anschauungen  auf  dem  Gebiete  der  anorganischen 
Chemie,  3rd  ed.,  Braunschweig,  1913. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT  33 

shown  by  W.  Kossel1  and  by  Langmuir2  that  this  idea  of  Werner 
is  in  perfect  harmony  with  the  electronic  conception  of  molecular 
compounds,  and  we  shall  give  later  in  this  book  a  direct 
proof  that  it  holds  for  proteins.  We  can,  therefore,  say  that  on 
the  acid  side  of  its  isoelectric  point  the  protein  particle  is  able 
to  add  acid  to  its  NH2  groups  in  the  following  form: 

pr>__NH2HCl 

+  HC1  =     K 
LiX- 


—  COOH  I*  v— COOH 


which  dissociates  electrolytically  into  a  protein  cation  and  an 
anion. 


COOH         A  ^— COOH 


While  our  symbol  indicates  only  one  NH2  group  in  the  mole- 
cule, it  is  probable  that  more  than  one  NH2  or  NH  group  is 
capable  of  adding  an  acid  molecule. 

The  simplification  in  the  general  chemistry  of  proteins  implied 
in  these  experiments  is  considerable.  We  only  need  to  remember 
that  on  the  alkaline  side  of  its  isoelectric  point  the  protein 
behaves  as  if  it  were  a  fatty  acid,  only  one  or  more  COOH 
groups  existing  in  a  chemically  active  form;  while  on  the  acid 
side  of  its  isoelectric  point  we  may  again  disregard  the  enormous 
protein  molecule  and  go  on  the  assumption  that  the  protein 
consists  only  of  one  or  a  number  of  NH2  groups,  each  capable  of 
adding  the  hydrogen  ion  of  an  acid. 

It  is  possible  though  not  proven  that  the  difference  in  the 
behavior  of  the  proteins  on  the  two  opposite  sides  of  the  isoelectric 
point  is  accompanied  by  an  intramolecular  change  in  the  protein 
molecule,  and  that  the  protein  anion  in  a  metal  proteinate  may 
be  considered  an  isomer  of  the  protein  cation  in  protein-acid  salt. 
Such  a  possibility  is  suggested  by  the  behavior  of  indicators  the 
electrolytic  dissociation  of  which  is  accompanied  by  an  intra- 
molecular change. 

When  we  mix  a  metal  gelatinate,  e.g.,  sodium  gelatinate,  with 
another  salt,  e.g.,  MgSO4,  the  Na  of  the  metal  gelatinate  can  be 

1  KOSSEL,  W.,  Ann.  d.  Physik,  vol.  49,  p.  229,  1916. 

2  LANGMUIR,  I.,  /.  Am.  Chem.  Soc.,  vol.  41,  p.  868,  1919, 

3 


34  THEORY  OF  COLLOIDAL  BEHAVIOR 

replaced  by  the  Mg  of  the  MgSO4  resulting  in  the  formation  of 
magnesium  gelatinate.  The  SO4,  however,  cannot  affect  the 
properties  of  Na  gelatinate  since  it  cannot  (or  can  practically  not) 
combine  with  the  gelatin.  When,  however,  we  mix  gelatin 
chloride  with  MgSO4,  only  the  SO4  can  affect  the  properties  of 
the  gelatin  salt,  since  the  SO4  can  replace  the  Cl  in  the  gelatin 
chloride  resulting  in  the  formation  of  gelatin  sulphate.  The  Mg, 
however,  cannot  (or  can  practically  not)  enter  into  combination 
with  gelatin  chloride  and  hence  cannot  affect  its  properties. 

When  we  alter  the  pH  of  a  gelatin-acid  salt,  e.g.,  gelatin 
chloride,  by  adding  alkali,  e.g.,  NaOH,  it  will  cease  to  be  gelatin 
chloride  as  soon  as  the  pH  is  4.7  because  at  this  pH  the  Cl  will  be 
given  off  by  the  gelatin  and  the  latter  will  be  transformed  into  the 
chemically  inert  isoelectric  or  non-ionogenic  gelatin  and  into 
NaCl.  The  isoelectric  gelatin  can  combine  practically  neither 
with  anions  nor  with  cations.  When  we  add  more  NaOH  so  that 
the  pH  is  >4.7,  Na  gelatinate  will  be  formed.  At  no  time  can 
metal  gelatinate  (e.g.,  Na  gelatinate)  and  gelatin-acid  salt  (e.g., 
gelatin  chloride)  exist  simultaneously  (except  in  traces  beyond 
the  limits  of  analytical  demonstration).  When  we  have  Na 
gelatinate  and  add  acid,  e.g.,  HC1,  the  gelatin  salt  will  give  off  its 
Na  and  become  isoelectric  gelatin  as  soon  as  pH  =  4.7.  This 
isoelectric  gelatin  is  chemically  inert  being  practically  unable  to 
combine  with  either  anion  or  cation.  When  we  add  more  HC1, 
gelatin  chloride  will  be  formed. 

These  experiments  show  that  proteins  behave  like  amphoteric 
electrolytes,  forming  definite  salts  with  acids  or  bases,  but  that 
they  cannot  combine  simultaneously  with  the  cation  and  the 
anion  of  a  neutral  salt.  The  idea  of  the  existence  of  adsorption 
compounds  between  non-ionized  molecules  of  proteins  and  mole- 
cules of  neutral  salts  is  not  in  harmony  with  these  experiments. 

In  1918  the  writer1  published  a  simple  method  of  preparing 
ash-free  proteins  based  on  the  fact  that  at  the  isoelectric  point 
proteins  can  combine  neither  with  anions  nor  with  cations. 
Hence,  if  we  wish  to  prepare  gelatin  or  casein  free  from  ionogenic 
impurities,  we  must  bring  these  proteins  in  powdered  form  to  the 
isoelectric  point  and  then  wash  them.  This  is  of  importance  for 
all  industries  using  proteins  as  well  as  for  scientific  work.  In  the 
,  J.,  J.  Gen.  PhysioL,  vol.  1,  p.  237,  1918-19. 


CORRECTNESS  OF  THE   CHEMICAL  VIEWPOINT          35 

writer's  work  isoelectric  protein  was  always  used  as  the  starting 
point  for  experiments. 

The  procedure  for  preparing  isoelectric  protein  is  simple 
enough.  It  is  only  necessary  to  determine  the  pH  of  a  given 
protein  solution  potentiometrically,  and  then  to  add  very  gradu- 
ally as  much  acid  or  alkali  as  is  required  to  bring  it  to  the  iso- 
electric point. 

The  following  method  was  used  to  prepare  larger  quantities 
of  approximately  isoelectric  gelatin:  50  gm.  of  commercial 
powdered  Cooper's  gelatin,  which  happened  to  have  a  pH  of 
6.0  to  7.0,  were  put  into  3,000  c.c.  of  M/128  acetic  acid  in  ajar 
at  10°C.,  and  stirred  frequently.  After  30  minutes  the  super- 
natant liquid  was  decanted  and  fresh  M/128  acetic  acid  at  10°C. 
was  added  to  equal  the  original  volume.  The  mass  was  fre- 
quently stirred,  and  after  30  minutes  the  acid  was  again  decanted 
and  replaced  by  an  equal  volume  of  distilled  water  at  5°C.  The 
gelatin  was  well  stirred  and  then  filtered  by  suction  through 
towel  cloth  in  a  Buchner  funnel.  It  was  then  washed  in  the 
funnel  five  times  each  with  1,000  c.c.  of  H2O  at  5°C.  After  all 
the  water  was  drained  off,  the  gelatin  was  transferred  from  the 
Buchner  funnel  into  a  large  beaker  which  was  then  heated  in  a 
water  bath  to  about  50°C.  till  the  gelatin  was  melted.  The 
concentration  of  the  gelatin  was  determined  by  evaporating 
to  dryness,  using  10  c.c.  of  the  melted  gelatin  in  an  electric  oven 
at  90  to  100°C.  for  24  hours. 

One  hundred  cubic  centimeters  of  a  1  per  cent  gelatin  solution 
prepared  in  this  way  had  no  more  than  1  mgm.  of  ash — appar- 
ently Ca3(PO4)2,  i-e..  the  salt  contained  in  the  solution  was 
M/30,000.  Salt  in  this  concentration  does  not  affect  the  physical 
properties  of  proteins,  such  as  osmotic  pressure,  viscosity,  P.D., 
swelling  or  precipitability  as  will  be  shown  in  this  volume.  The 
following  is  a  result  of  an  ash  determination  made  by  Dr.  D.  I. 
Hitchcock  on  a  sample  of  gelatin  selected  at  random.  The  stock 
solution  contained  12.69  per  cent  gelatin. 

SAMPLE  No.  1  SAMPLE  No.  2 

Volume  of  solution 20  c.c.  10  c.c. 

Weight  of  dry  gelatin 2.535  gm.  1.269  gm. 

Weight  of  ash 0.0024  gm.  0.0012  gm. 

Obtained  qualitative  tests  for  Fe+4+,  "Ca^,  and  PO^,  negative  tests  for 
Cl-  and  SOr. 


36  THEORY  OF  COLLOIDAL  BEHAVIOR 

Miss  Field1  has  shown  that  by  carrying  the  washing  process  a 
step  further  the  last  traces  of  ash  can  be  removed  from  the 
powdered  gelatin.  In  bringing  powdered  gelatin  to  the  iso- 
electric  point  and  washing  with  water  of  the  pH  of  the  isoelectric 
point  we  can  quickly  make  the  gelatin  completely  ash-free.  If 
the  protein  is  soluble  at  this  point  (as  is  the  case  with  crystalline 
egg  albumin)  it  is  only  necessary  to  carry  out  the  dialysis  at  the 
pH  of  the  isoelectric  point  to  obtain  the  protein  free  from  iono- 
genic  impurities.2 

This  fact  is  a  further  support  of  our  contention  that  at  the 
isoelectric  point  proteins  can  combine  with  neither  anion  nor 
cation. 

We  may  call  attention  to  one  interesting  fact  which  is  in 
harmony  with  these  results.  It  has  always  been  known  that 
pepsin  digestion  occurs  in  nature  in  an  acid  medium.  The 
reason  for  this  connection  of  an  acid  reaction  with  pepsin  digestion 
was  cleared  up  by  Northrop3  who  found  that  the  hydrogen  ion 
concentration  at  which  pepsin  commences  to  act  on  a  protein 
varies  with  the  isoelectric  point  of  the  protein  and  that  the  action 
always  occurs  on  the  acid  side  of  the  isoelectric  point.  It 
seems  to  follow  from  the  experiments  of  Pekelharing  and  Ringer4 
that  pepsin  is  an  anion  like  Cl  which  can  only  combine  with  a 
positive  protein  ion.  This  combination  between  pepsin  and 
positive  protein  ion  seems  to  be  the  prerequisite  for  the  falling 
apart  (or  digestion)  of  the  protein  ion. 

1  FIELD,  A.  M.,  J.  Am.  Chem.  Soc.,  vol.  43,  p.  667,  1921. 

2  Miss  Field's  paper  as  well  as  the  writer's  paper  referred  to  were  over- 
looked by  C.  R.  SMITH    (J.  Am.  Chem.  Soc.,  vol.  43,  p.  1350,  1921)  who 
also  describes  a  method  of  preparing  ash-free  gelatin. 

3  NORTHROP,  J.  H.,  J.  Gen.  Physiol.,  vol.  3,  p.  211,  1920-21. 

4  PEKELHARING,  C.  A.  and  RINGER,  W.  E.,  Z.  physiol  Chem.,  vol.  75, 
p.  282,  1911. 


CHAPTER  III 

METHODS  OF  DETERMINING  THE  ISOELECTRIC  POINT 
OF  PROTEIN  SOLUTIONS 

The  results  of  the  preceding  chapter  make  it  clear  that  when- 
ever work  with  amphoteric  electrolytes  is  contemplated  it 
becomes  necessary  to  ascertain  first  the  isoelectric  point  of  the 
substance,  since  at  the  isoelectric  point  the  material  can  be  most 
easily  freed  from  ionogenic  impurities.  There  can  be  no  doubt 
that  many  of  the  substances  exhibiting  colloidal  behavior  are 
amphoteric  electrolytes. 

Hardy  and  Michaelis  determined  the  isoelectric  point  by 
observations  on  the  migration  of  particles  in  the  electrical  field. 
There  are  other  methods  available  for  this  purpose,  some  of 
which  are  often  more  convenient  than  Hardy's  original  method. 
These  methods  are  based  on  the  fact  that  at  the  isoelectric  point 
the  osmotic  pressure,  the  viscosity,  the  amount  of  alcohol  required 
for  precipitation,  the  conductivity,  the  swelling,  the  P.D.  are  all 
a  minimum.  When  the  curves  representing  the  values  of  these 
properties  are  plotted  as  ordinates  over  the  pH  as  abscissae,  the 
curves  show  a  sharp  drop  at  the  isoelectric  point.  If,  therefore, 
a  protein  is  brought  to  different  pH  by  adding  acid  or  alkali,  and 
if  any  of  the  properties  mentioned  is  determined,  the  approximate 
position  of  the  isoelectric  point  can  be  inferred  from  the  minimum 
point  of  the  property  which  is  used  as  a  test.  The  writer  has 
found  it  most  convenient  to  use  osmotic  pressure  experiments  in 
the  case  of  proteins. 

The  following  older  experiment  by  the  writer  may  serve  as  an 
illustration.1  A  number  of  doses  each  containing  1  gm.  of  finely 
powdered  Cooper's  gelatin  which  had  a  pH  of  a  little  over  7.0 
and  consisted  partly  of  Ca  gelatinate  were  put  for  30  minutes  at 
15°C.  into  beakers  containing  100  c.c.  of  HBr  of  different  con- 
centrations, varying  from  M/8  to  M/8,192;  and  as  a  control  1  gm. 
of  gelatin  was  put  for  30  minutes  at  15°C.into  100  c.c.  of  distilled 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  1,  p.  363,  1918-19. 

37 


38 


THEORY  OF  COLLOIDAL  BEHAVIOR 


Rej 

*ion  of  GelaTin-Br 

Isoelectrjc 
point      Region  of  Gelatin 

100 
90 
80 
70 
60 
50 
40 
30 
20 
10 
0 
130 
120 
110 
100 
90 
80 
70 
60 
175 
150 
1Z5 
100 
75 
50 
IS 
0 
4 
3 
Z 
1 
0 
3 
Z 
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0 

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)  — 

Vis 

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y 

Soc 

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I  PC 
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HBr         M       M       M       M       M  —  M: 
cone.       8      16     32     64    »TZ5f 

-M       M        M       M       M       M       f. 
*&    1024   Z048  4096  mi  1638* 

pH      41     4.1    42    42    444'5454J49    52    5.4    i5    56    S6   56 

FIG.  3. — Showing  that  the  physical  properties  of  gelatin  are  a  minimum  at  the 

isoelectric  point. 


ISOELECTRIC  POINT  OF  PROTEIN  SOLUTIONS  39 

water.  The  powdered  gelatin  was  then  put  into  a  cylindrical 
funnel  and  the  acid  allowed  to  drain  off.  The  powdered  gelatin 
in  the  funnel  was  then  perfused  six  or  eight  times,  with  constant 
stirring,  each  time  with  25  c.c.  cold  water — i.e.,  water  not  above 
5°C. — to  remove  the  excess  of  acid  and  the  salts.  The  water 
must  be  cold  to  prevent  the  powdered  granules  from  coalescing 
since  otherwise  the  washing  would  be  incomplete.  After  the 
liquid  was  drained  off  from  the  filter,  the  volume  (i.e.,  the  rela- 
tive swelling  of  the  gelatin)  was  measured;  then  the  gelatin  was 
melted  by  heating  to  45°C.  and  enough  water  was  added  to  bring 
the  volume  in  each  case  to  100  c.c.  Then  the  conductivity, 
osmotic  pressure,  and  viscosity  were  measured  in  a  way  to  be 
described  in  a  later  chapter,  and  the  pH  was  also  determined, 
either  colorimetrically  (which  gives  fairly  accurate  results  with 
gelatin  but  not  with  the  other  proteins)  or  preferably  with  the 
hydrogen  electrode.  In  the  experiment  represented  in  Fig.  3  the 
pH  was  measured  colorimetrically.  A  glance  at  the  figure  shows 
that  the  ordinates  of  the  curves  representing  the  values  for 
osmotic  pressure,  conductivity,  swelling,  etc.,  drop  very  sharply 
at  pH  4.7,  i.e.,  the  isoelectric  point  of  gelatin.  By  this  method 
the  approximate  location  of  the  isoelectric  point  can  be  recognized 
at  a  glance  from  the  osmotic  pressure  measurements,  the  conduc- 
tivity measurements,  etc.  The  P.D.  measurements  would  also 
show  a  minimum  at  the  isoelectric  point. 

The  lowest  curve  in  Fig.  3  represents  titration  for  Br.  Gelatin 
should  exist  in  the  form  of  gelatin  bromide  only  on  the  acid  side  of 
the  isoelectric  point  and  titration  for  Br  should  be  negative 
when  the  pH  is  above  4.7.  The  curve  shows  that  no  Br  was 
found  when  pH  was  equal  or  greater  than  4.7;  while  it  was  found 
on  the  acid  side  increasing  in  quantity  the  lower  the  pH.  On  the 
alkaline  side  of  the  isoelectric  point  the  gelatin  existed  still  in 
the  state  of  Ca  gelatinate.  In  this  experiment  the  mass  of  the 
gelatin  was  diminished  by  solution  and  washing  to  0.8  gm.  or 
possibly  a  little  less. 

We  shall  see  later,  that  when  powdered  gelatin  is  put  into  an 
acid  solution,  e.g.,  N/100  or  N/1,000  HBr,  the  concentration  of 
the  acid  inside  the  gelatin  granules  is  considerably  lower  than  in 
the  outside  solution.  This  is  due  to  the  establishment  of  a 
Donnan  equilibrium. 


CHAPTER     IV 

QUANTITATIVE  PROOF  OF  THE  CORRECTNESS  OF  THE 
CHEMICAL  VIEWPOINT 

1.  The  qualitative  experiments  of  the  second  chapter  did 
not  permit  us  to  decide  whether  ions  combine  with  proteins 
stoichiometrically  (i.e.,  by  the  purely  chemical  forces  of  primary 
valency),  or  according  to  the  empirical  rule  of  adsorption,  as  is 
assumed  in  colloid  chemistry.  A  decision  can  be  rendered  by 
titration  experiments.1 

The  titrations  required  for  this  proof  differ  from  those  usually 
performed  in  chemistry.  In  the  usual  chemical  work  titration 
is  carried  to  the  point  of  neutrality,  i.e.,  pH  near  7.0.  Proteins, 
however,  are  amphoteric  electrolytes,  the  isoelectric  point  of 
which  is  generally  different  from  neutrality.  Gelatin  and  casein 
act  as  bases  for  a  pH  below  4.7,  and  if  we  wish  to  ascertain  how 
much  of  a  certain  acid  1  gm.  of  isoelectric  gelatin  can  bind  we  have 
to  titrate  to  a  pH  below  4.7.  In  doing  this,  we  must  also  remem- 
ber that  at  such  a  high  hydrogen  ion  concentration  only  strong 
dibasic  acids,  like  H2SO4,  continue  to  dissociate  both  H  ions, 
while  weaker  dibasic  or  tribasic  acids,  e.g.,  H3PO4,  are  only  able 
to  split  off  one  H  ion,  acting  therefore  like  monobasic  acids. 

Our  solutions  contain  generally  1  gm.  of  isoelectric  protein  in 
100  c.c.,  and  such  solutions  will  be  called  1  per  cent  protein 
solutions.  When  1  per  cent  solutions  of  albumin  sulphate  or  1  per 
cent  solutions  of  gelatin  chloride  are  mentioned,  this  means  that 
1  gm.  of  originally  isoelectric  albumin  or  gelatin  was  in  100  c.c.  of 
the  solution.  The  concentration  of  the  stock  solution  of  isoelec- 
tric gelatin,  albumin,  or  casein  was  determined  by  measuring  the 
dry  weight  of  the  solution. 

When  different  quantities  of  0.1  N  acid,  e.g.,  HC1,  are  added 
to  the  same  quantity  of  protein,  e.g.,  I  gm.  of  isoelectric  gelatin 
or  crystalline  egg  albumin,  bringing  the  volume  of  the  solution 

1LOEB,  J.,  J.Gen.  Physiol.,  vol.  1,  p.  559, 1918-19;  vol.  3,  p.  85,  1920-21. 

40 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          41 

always  to  100  c.c.,  it  is  found  that  the  resulting  hydrogen  ion 
concentration  of  the  solution  is  different  from  the  pH  which  is 
found  when  the  same  amount  of  acid  is  added  to  the  same  quan- 
tity of  pure  water.  This  is  due  to  the  fact  that  part  of  the  acid 
combines  with  the  protein  as  originally  suggested  by  Bugarszky 
and  Liebermann.1  On  the  basis  of  Werner's2  idea  the  HC1  should 
combine  with  the  NH2  groups  of  the  protein  molecule  in  the  same 
way  as  if  it  were  added  to  NH3,  thus  forming  a  salt  of  the  type 
RNH3C1.  This  is  intelligible  on  the  basis  of  the  recent  theories 
of  G.  N.  Lewis,3  Kossel,4  and  Langmuir.5  Gelatin  chloride  may 
therefore  be  expected  to  dissociate  electrolytically  in  the  following 
way: 

Gelatin  NH3O1  ^  gelatin  NH3  +  Cl 

Hence,  the  concentration  of  the  free  Cl  ions  in  a  watery  solution 
of  HC1  should  remain  the  same  if  a  small  amount  of  isoelectric 
gelatin  is  added,  provided  the  electrolytic  dissociation  is  complete. 
This  was  tested  by  comparing  the  pCl  of  HC1  solutions  with  and 
without  gelatin  (Table  I).  Both  the  pH  and  the  pCl  were 
measured  electrometrically.  Table  I  shows  that  this  pCl  was 
in  solutions  of  HC1  without  gelatin  always  identical  with  the 
pH  of  the  same  solution.  In  a  second  set  of  experiments  the 
same  HC1  solutions  contained  each  1  gm.  of  isoelectric  gelatin  in 
100  c.c.,  and  the  pH  and  pCl  in  these  1  per  cent  solutions  of 
gelatin  chloride  were  also  determined  after  the  reaction  was  com- 
plete. The  reader  will  notice  from  Table  I  that  the  values  for 
pCl  of  the  watery  solutions  are  within  the  limits  of  accuracy  of 
the  determinations  identical  with  those  found  in  the  gelatin 
solutions  containing  the  same  amount  of  acid.  The  pH,  however, 
is  different  in  the  aqueous  and  in  the  1  per  cent  gelatin  solutions, 

1  BUGARSZKY,  S.  and  LIEBERMANN,  L.,  Arch.  ges.  Physiol.,  vol.  72,  p. 
51,  1898. 

2  WERNER,  A.,  "  Neuere  Anschauungen  auf  dem  Gebiete  der  anorganischen 
Chemie,"  3rd  ed.,  Braunschweig,  1913. 

3  LEWIS,  G.  N.,  J.  Am.  Chem.  Soc.,  vol.  38,  p.  762,  1916. 

4  KOSSEL,  W.,  Ann.  Physik,  vol.  49,  p.  229,  1916. 

5  LANGMUIR,  I.,  J.  Am.  Chem.  Soc.,  vol.  41,  p.  868,  1919;  vol.  42,  p.  274, 
1920. 


42 


THEORY  OF  COLLOIDAL  BEHAVIOR 


since,  in  the  latter,  part  of  the  H  ions  of  the  free  HC1  added 

+ 

becomes  part  of  the  complex  gelatin  cation,  gelatin-NH3.  The 
figures  in  Table  I  then  prove  that  a  strong  acid,  like  HC1,  com- 
bines with  the  protein  according  to  Werner's  ideas. 

TABLE  I 


Cubic  centi- 

Solution containing  no 

Solution  containing  1  gm.  of 

meters  of 

gelatin 

isoelectric  gelatin  in  100  c.c. 

0.1  N  HC1 

in  100  c.c. 

solution 

pH 

pCl 

pH 

pCl 

2 

2.72 

2.72 

4.2 

2.68 

3 

2.52 

2.54 

4.0 

2.53 

4 

2.41 

2.39 

5 

2.31 

2.29 

3.60 

2.33 

6 

2.24 

2.26 

3.41 

2.25 

7 

2.16 

2.18 

3.23 

2.18 

8 

2.11 

2.12 

3.07 

2.11 

10 

2.01 

2.01 

2.78 

2.025 

15 

1.85 

1.85 

2.30 

1.845 

20 

1.72 

1.76 

2.06 

1.76 

30 

1.55 

1.59 

1.78 

1.60 

40 

1.43 

1.47 

1.61 

1.47 

It  was  found  that  whenever  the  same  amount  of  acid  was  added 
to  the  same  amount,  e.g.,  1  gm.,  of  originally  isoelectric  gelatin, 
making  up  the  volume  to  100  c.c.,  the  pH  of  the  solution  was 
always  the  same ;  so  that  we  can  say  how  much  Cl  is  in  combina- 
tion with  the  protein  if  we  know  the  pH  of  the  gelatin  chloride 
solution.  The  lower  the  pH,  the  more  chloride  enters  into  com- 
bination with  the  protein,  until  finally,  all  the  protein  is  trans- 
formed into  protein  chloride. 

It  seems  that  when  an  acid,  e.g.,  HC1,  is  added  to  isoelectric 
gelatin  (or  any  other  isoelectric  protein),  an  equilibrium  is 
established  between  free  HC1,  protein  chloride,  and  non-ionogenic 
(or  isoelectric)  protein;  when  alkali  is  added  to  isoelectric  gelatin, 
an  equilibrium  is  established  between  metal  proteinate,  non- 
ionized  protein,  and  free  alkali  (above  pH  4.7).  Similar  results 
had  been  obtained  by  S0rensen.1 

1  S0RENSEN,  S.  P.  L.,  Studies  on  proteins :  Compt.  rend.  trav.  Lab.  Carlsberg, 
vol.  12,  Copenhagen,  1915-17. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          43 

It  can  be  shown  by  titration  experiments  that  acids  and  bases 
combine  with  proteins  in  the  same  way  as  they  combine  with 
crystalline  compounds,  namely,  by  the  purely  chemical  forces 
of  primary  valency.  It  is  known  that  a  weak  dibasic  or  tribasic 
acid  gives  off  one  hydrogen  ion  more  readily  than  both  or  all 
three,  and  that  it  depends  on  the  hydrogen  ion  concentration  of 
the  solution  whether  one  or  two  or  three  H  ions  are  dissociated 
from  a  tribasic  acid.  Thus  H3PO4  will  give  off  only  one  H  ion 
as  long  as  the  pH  is  below  4.6.  Oxalic  acid,  which  is  a  stronger 
acid,  will  act  like  a  monobasic  acid  below  a  pH  of  about  3.0,1 
while  above  this  pH  it  acts  more  and  more  like  a  dibasic  acid. 
In  a  strong  dibasic  acid,  like  H2SO4,  both  H  ions  are  held  with  so 
small  an  electrostatic  force  that  even  at  a  pH  of  3.0  or  consider- 
ably below  the  acid  acts  as  a  dibasic  acid.  If  the  forces  which 
determine  the  reaction  between  these  acids  and  proteins  are 
purely  chemical,  it  would  follow  that  three  times  as  many  cubic 
centimeters  of  0.1  N  H3PO4  should  be  required  to  bring  100  c.c. 
of  1  per  cent  solution  of  isoelectric  gelatin  to  a  given  pH  below 
4.6,  e.g.,  3.0,  as  are  required  in  the  case  of  HNO3  or  HC1;  while  it 
should  require  just  as  many  cubic  centimeters  of  0.1  N  H2SO4  as 
of  0.1  N  HC1.  Twice  as  many  cubic  centimeters  of  0.1  N  oxalic 
acid  should  be  required  to  bring  isoelectric  gelatin  to  a  pH  of 
3.0  or  below,  as  are  required  in  the  case  of  HC1.  It  can  be  shown 
that  these  predictions  are  true.2 

2.  Crystalline  egg  albumin  was  prepared  according  to  S0rensen's 
method,3  and  crystallized  three  times.  The  only  difference  in 
procedure  was  in  the  dialysis.  Instead  of  putting  the  water 
under  negative  pressure,  as  was  done  by  S0rensen,  pressure  was 
put  on  the  egg  albumin  by  attaching  a  long  glass  tube  full  of 
water  to  the  dialyzing  bag  so  that  the  solution  was  under  about 
150  cm.  water  pressure  during  dialysis.  This  was  necessary  to 
avoid  too  great  an  increase  in  volume.  The  same  stock  solution 

1  HILDEBRAND,  J.   H.,   J.  Am.   Chem.  Soc.,  vol.  35,  p.  847,  1913.     See 
also  MICHAELIS,  L.,   "Die  Wasserstoffionenkonzentration,"   Berlin,   1914; 
CLARK,  W.  M.,  "The  Determination  of  Hydrogen  Ions,"  Baltimore,  1920. 

2  The  experiments  to  be  described  are  from  LOEB,  J.,  J.  Gen.  Physiol., 
vol.  3,  p.  85,  1920-21. 

3  S^RENSEN,  S.  P.  L.,  Studies  on  proteins:  Compt.  rend.  trav.Lab.  Carlsberg, 
vol.  12,  Copenhagen,  1915-17. 


44 


THEORY  OF  COLLOIDAL  BEHAVIOR 


of  albumin  served  for  all  the  experiments  and  was  diluted  before 
the  experiment  to  a  1  per  cent  solution.     The  concentration  of 


pH    2.0   22  2.4    26   2.8  3.0  3.2   3.4  3.6  3.8  4.0   4.2  4.4  4.6 


FIG.  4. — The  ordinates  represent  the  number  of  c.c.  of  0.1  N  HC1,  H2SO4, 
oxalic,  and  phosphoric  acids  required  to  bring  1  gm.  of  isoelectric  crystalline 
egg  albumin  to  the  pH  indicated  on  the  axis  of  abscissae.  Enough  H2O  was 
added  to  bring  the  albumin  and  acid  to  a  volume  of  100  c.o.  For  the  same  pH 
the  ordinates  for  HC1,  HzSC^,  and  phosphoric  acid  are  approximately  as  1:1:3. 
The  ratio  of  HC1  to  oxalic  acid  is  a  little  less  than  1 : 2  when  pH  is  >  3.0. 

ammonium  sulphate  left  in  the  solution  was  between  M/ 1,000  and 
M/2,000.     The  pH  of  the  stock  solution  was  about  5.20.     By 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          45 

adding  about  1  c.c.  0.1  N  HC1  to  100  c.c.  of  a  1  per  cent  solution 
of  this  albumin  the  solution  was  brought  to  the  isoelectric  point 
of  the  egg  albumin,  which  is  according  to  S0rensen  at  pH  =  4.8. 

The  1  per  cent  solutions  were  made  up  with  different  quantities 
of  acid  (or  alkali)  and  the  pH  of  the  albumin  solution  was 
determined  electrometrically.  In  Fig.  4  are  plotted  the  titration 
curves  in  which  the  pH  are  the  abscissae  while  the  ordinates  are 
the  cubic  centimeters  of  0.1  N  acid  required  to  bring  the  1  per 
cent  solutions  of  originally  isoelectric  crystalline  egg  albumin  to 
different  pH.  The  curves  represent  these  titration  values  for 
four  acids,  HC1,  H2SO4,  H3PO4,  and  oxalic  acid.  Beginning 
with  the  lowest  curve,  we  notice  that  the  curve  is  the  same  for 
0.1  N  HC1  and  0.1  N  H2SO4,  since  both  are  strong  acids;  or,  in 
other  words,  H2SO4  combines  in  equivalent  proportions  with  egg 
albumin.  The  curve  for  H3PO4  is  the  highest  curve  and  if  we 
compare  the  values  for  H3PO4  with  those  for  HC1  (or  H2SO4) 
we  notice  that  for  each  pH  the  ordinate  for  H3P04  is  as  nearly 
three  times  as  high  as  that  for  HC1  as  the  accuracy  of  our  experi- 
ments permits.  This  means  that  phosphoric  acid  combines 
with  albumin  (inside  of  the  range  of  pH  of  our  experiment)  in 
molecular  proportions  and  that  the  anion  of  albumin  phosphate 
is  the  monovalent  anion  H2PO4. 

The  values  for  oxalic  acid  are  for  pH  below  3.2  almost  but  not 
quite  twice  as  high  as  those  for  HC1,  indicating  that  for  these 
values  of  pH  oxalic  acid  combines  to  a  greater  extent  in  molecular 
and  only  to  a  small  extent  in  equivalent  proportions  with 
albumin. 

These  combining  ratios  of  the  four  acids  named  with  crystalline 
egg  albumin  are,  therefore,  the  same  as  those  which  would  be 
found  if  we  substituted  the  crystalloidal  base  NH3  for  the  colloid 
egg  albumin,  titrating  in  the  same  range  of  pH. 

From  the  curves  just  discussed,  the  amount  of  acid  in  combi- 
nation with  1  gm.  of  originally  isoelectric  crystalline  egg  albumin 
in  a  1  per  cent  solution  of  this  protein  at  different  pH  can  easily 
be  calculated.  Let  us  assume  the  acid  added  to  isoelectric 
albumin  to  be  HC1.  If,  e.g.,  at  pH  3.0,  6  c.c.  of  0.1  N  HC1  are 
contained  in  100  c.c.  of  the  1  per  cent  solution  of  the  originally 
isoelectric  albumin  (as  indicated  in  Fig.  4),  part  of  the  acid  is  in 
combination  with  the  albumin  and  part  is  free.  How  much  is 


46 


THEORY  OF  COLLOIDAL  BEHAVIOR 


free  is  known  from  the  pH  of  the  albumin  chloride  solution, 
namely,  1  c.c.,  since  in  the  example  selected  the  pH  is  3.0  (Fig. 
4).  If  1  c.c.  is  deducted  from  6  c.c.  it  is  found  that  at  pH  3.0 


19 
18 
17 
16 
15 
14 
13 
12 

10 
9 
8 


pH  1.8  2.0   2.2  2.4  2.6   2.8  3.0   3.2  3.4  3.6  3.8  40  4.2  44  4.6  4.8 

FIG.  5.— Method  of  determining  the  amount  of  acid  in  combination  with  1  gm. 
of  albumin  from  titration  curve  and  pH  curve. 

5  c.c.  of  0.1  N  HC1  are  in  combination  with  1  gm.  of  originally 
isoelectric  crystalline  egg  albumin  in  100  c.c.  solution  (Fig.  5). 
A  curve  is  constructed  in  which  the  abscissa  are  the  pH  while  ^he 
ordinates  are  the  cubic  centimeters  of  0.1  N  HC1  contained  in  100 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          47 
c.c.  of  a  watery  solution,  without  protein.    If  the  ordinatesof  this 


Z2 
21 
20 
19 
18 
IT 
16 
15 
14 
13 
12 
11 
10 


8 


[ 

\ 

1 

\ 

\ 

4 

\ 

\ 

:c.  acid  combined 
rith  1  gm.  of  originally 
soelectric  egg  albumi 
in  100  cc.  solution 

\ 

( 

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9 

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pHl8   a.O   2.2   2.4  26    28   3.0   3.2    3.4  36   3.8   40  42  4.4  46 

Fio.  6. — Proof  of  the  stoichiometrical  character  of  the  combination  of  acids 
with  isoelectric  albumin.  The  same  mass  of  albumin  com  bines  with  three  times 
as  many  c.c.  of  0.1  N  H3PO4  as  with  HClor  H 2SO 4 ;  and  with  twice  as  many  c.c. 
of  0.1  N  oxalic  acid  below  pH  3.0. 

latter  curve  are  deducted  from  the  ordinates  of  the  titration 


48  THEORY  OF  COLLOIDAL  BEHAVIOR 

curve  in  Fig.  4  containing  1  per  cent  of  originally  isoelectric 
albumin  chloride  we  get  a  curve  whose  ordinates  give  the  number 
of  cubic  centimeters  of  0.1  N  HC1  in  actual  combination  with  1  gm. 
of  originally  isoelectric  albumin  in  100  c.c.  solution  (middle  curve 
Fig.  5). 

Figure  6  contains  the  curves  whose  ordinates  give  the  amount 
of  cubic  centimeters  of  0.1  N  HC1,  H2S04,  H2C204,  and  H3PO4 
in  combination  with  1  gm.  of  originally  isoelectric  egg  albumin  at 
different  pH.  It  appears  again  that  the  curves  for  HC1  and  H2SO4 
practically  coincide  as  the  purely  chemical  theory  demands,  that 
the  oxalic  acid  curve  is  higher,  and  that  the  phosphoric  acid 
curve  is  still  higher.  What  is  of  greater  importance  is  that  for 
the  same  pH  the  ordinates  of  the  H3P04  curve  are  always  approxi- 
mately three  times  as  high  as  the  ordinates  of  the  curves  for  HC1 
and  H2SO4. 

The  results  in  Table  II  show  the  actual  numbers  of  cubic 
centimeters  of  each  of  the  four  acids  in  combination  with  1  gm. 
of  originally  isoelectric  crystalline  egg  albumin  in  100  c.c.  solution. 
The  values  for  HC1  and  H2S04  are  identical.  Those  for  H3PO4 
are  within  the  limits  of  accuracy  always  three  times  as  large  as 
those  for  HC1.  Thus  at  pH  4.0,  1.7  c.c.  of  0.1  N  HC1  or  H2SO4 
are  combined  with  1  gm.  of  albumin,  while  5.3  c.c.  of  0.1  N  H3PO4 
are  in  combination;  at  3.4,  3.5  c.c.  of  0.1  N  HC1  or  H2SC>4  and 
10.6  c.c.  of  0.1  N  H3PO4. 

In  the  case  of  oxalic  acid,  we  notice  that  at  pH  above  3.6  the 
number  of  cubic  centimeters  of  0.1  N  oxalic  acid  in  combination 
with  1  gm.  of  albumin  is  less  than  twice  that  of  HC1  and  that  the 
difference  is  the  greater  the  higher  the  pH.  At  pH  =  3.2  and 
below  practically  twice  as  many  cubic  centimeters  of  oxalic  acid 
are  at  the  same  pH  in  combination  with  1  gm.  of  originally 
isoelectric  albumin  as  are  of  HC1.  Thus  at  pH  2.6,  6.7  c.c.  of  0.1 
N  HC1  and  13.3  c.c.  of  0.1  N  oxalic  acid  are  in  combination  with 
1  gm.  of  albumin;  at  pH  3.0,  5.0  c.c.  of  0.1  N  HC1  and  9.5  c.c.  of 
0.1  N  oxalic  acid.  These  figures  correspond  to  the  results  to  be 
expected  on  the  basis  of  Hildebrand's  titration  experiments 
against  inorganic  bases.  These  titration  experiments  then  leave 
no  doubt  that  these  acids  combine  with  proteins  in  the  same 
stoichiometric  way  as  they  combine  with  crystalloids.  That 
these  simple  facts  had  not  been  discovered  earlier  is  the  con- 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT 


49 


TABLE  II. — CUBIC  CENTIMETERS  OF  0.1  N  ACID  IN  COMBINATION   WITH 

1  GM.  OF  ORIGINALLY  ISOELECTRIC    CRYSTALLINE  EGG  ALBUMIN  IN 

100  c.c.  SOLUTION 


PH 

HC1, 
cubic 
centimeters 

H2S04, 
cubic 
centimeters 

Oxalic  acid, 
cubic 
centimeters 

H3P04, 

cubic 
centimeters 

4.2 

1.15 

1.15 

1.8 

3.8 

4.0 

1.7 

1.7 

2.6 

5.3 

3.8 

2.3 

2.3 

3.7 

6.8 

3.6 

2.9 

2.9 

5.0 

8.6 

3.4 

3.5 

3.5 

6.3 

10.6 

3.2 

4.2 

4.3 

8.0 

13.1 

3.0 

5.0 

5.1 

9.5 

16.1 

2.8 

5.8 

5.9 

11.1 

19.3 

2.6 

6.7 

6.5 

13.3 

22.9 

2.4 

7.6 

7.0 

16.0 

sequence  of  the  failure  of  the  workers  to  consider  the  hydrogen 
ion  concentration  of  their  solutions.  Had  this  been  done,  nobody 
would  have  thought  of  suggesting  that  acids  combine  with  pro- 
teins according  to  the  adsorption  formula. 

These  titration  experiments  are  of  especial  value  for  the  reason 
that  crystalline  egg  albumin  is  for  the  present  probably  the 
purest  protein  available. 

The  same  proof  can  be  furnished  in  the  case  of  other  proteins, 
e.g.,  gelatin.  A  stock  solution  of  isoelectric  gelatin  was  used  for 
the  experiment.  The  isoelectric  gelatin  was  prepared  by  putting 
the  powdered  gelatin  of  pH  7.0  into  M/128  acetic  acid  (100  c.c.  of 
11/128  acid  for  1  gm.  of  gelatin)  for  1  hour  at  15°C.,  and  then 
washing  four  or  five  times  with  cold  water  (5°C.).  An  8  per  cent 
stock  solution  was  prepared ;  the  concentration  of  the  gelatin  was 
ascertained  by  a  determination  of  the  dry  weight.  To  50  c.c.  of  a 
2  per  cent  solution  of  isoelectric  gelatin  were  added  different 
quantities  of  acid  and  the  volume  made  up  to  100  c.c.  by  adding 
enough  H20,  usually  of  a  pH  of  about  5.6.  It  was  ascertained 
how  many  cubic  centimeters  of  0.1  N  different  acids  were  required 
to  bring  1  gm.  of  isoelectric  gelatin  in  a  1  per  cent  solution  to  the 
same  pH. 

4 


50 


THEORY  OF  COLLOIDAL  BEHAVIOR 


In  Fig.  7  the  abscissae  are  the  pH  while  the  ordinates  are  the 
number  of  cubic  centimeters  of  0.1  N  HC1,  H2SO4,  H2  oxalate, 


pHlfi   2.0    2.2   2.4   2.6    ZQ   3.0    3.2  3.4   3.6    3.8  4.0   42   44  46 


FIG.  7.  —  Titration  curve  for  1  per  cent  solution  of  originally  isoelectric  gelatin, 
proving  the  stoichiometrical  character  of  combination  of  acids  with  gelatin 
(see  legend  under  Fig.  6). 

and  H3PO4  contained  in  100  c.c.  solution  of  originally  isoelectric 
gelatin  to  the  same  pH, 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          51 

It  is  again  obvious  that  the  curves  for  HC1  and  H2SO4  are 
practically  identical  while  the  ordinates  of  the  curve  for  H3PO4 


20 
19 
18 
17 
16 
15 
14 
13 
12 
11 
10 


\ 

4 

I 

\ 

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)c.  acid  combined    - 
rith  Ifim.  of  originallyi 
.5oelectric  gelatin 
n  lOOcc.  solution    - 

\ 

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4 

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( 

LC 

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% 

^ 

^     t 

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c. 

WA 

^ 

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2.0    22    £.4  2.6   2.8   3.0   3.Z    3.4   3.6    3.6  4.0   4.2  44  4.6 


FIG.    8.  —  Combination   curve   of   acids   with   gelatin,    confirming   the   stoichio- 
metrical  character  of  the  combination. 

are  approximately  three  and  those  for  oxalic  acid  about  twice  as 
high  as  those  for  HC1  or  H2SO4  for  the  same  pH,  as  long  as  the 
pH  is  below  3.2;  while  above  3.2  the  curve  for  oxalic  acid  deviates 


52 


THEORY  OF  COLLOIDAL  BEHAVIOR 


the  more  from  that  ratio  the  higher  the  pH,  as  the  theory 
demands. 

The  curves  in  Fig.  8  represent  the  values  for  the  cubic  centi- 
meters of  0.1  N  acid  found  in  combination  with  1  gm.  of  originally 
isoelectric  gelatin  in  100  c.c.  solution  at  different  pH.  The 
results  are  tabulated  in  Table  III.  The  table  shows  that 
within  the  limits  of  accuracy  of  the  experiments,  at  the  same  pH 
approximately  equal  numbers  of  cubic  centimeters  of  0.1  N  HC1 
and  0.1  N  H2S04  are  in  combination  with  1  gm.  of  originally 
isoelectric  gelatin  in  100  c.c.  solution,  while  about  three  times  as 
many  cubic  centimeters  of  0.1  N  H3PO4  are  in  combination.  The 
number  of  cubic  centimeters  of  0.1  N  oxalic  acid  in  combination 
with  1  gm.  of  gelatin  is  less  than  twice  that  of  HC1  as  long  as  the 
pH  is  above  3.0,  while  below  3.0  the  combining  ratio  of  the  two 
acids  is  approximately  as  1:2,  as  the  theory  demands. 

TABLE  III. — CUBIC  CENTIMETERS  OF  0.1  N  ACID  IN  COMBINATION  WITH 
1  GM.  OF  ORIGINALLY  ISOELECTRIC  GELATIN  IN  100  c.c.  SOLUTION 


HC1, 

H2S04, 

Oxalic  acid, 

H3P04, 

pH 

cubic 

cubic 

cubic 

cubic 

centimeters 

centimeters 

centimeters 

centimeters 

4.0 

2.7 

3.9 

6.95 

3.8 

3.9 

3.75 

5.5 

9.4 

3.6 

4.8 

4.8 

7.3 

12.3 

3.4 

5.6 

5.75 

9.1 

15.2 

3.2 

6.4 

6.75 

11.0 

18.0 

3.0 

7.2 

7.5 

13.15 

20.7 

2.8 

7.9 

8.25 

15.3 

23.6 

2.6 

8.35 

8.8 

17.1 

26.2 

2.4 

8.5 

9.3 

18.0 

These  experiments  corroborate  our  conclusion  that  acids 
combine  stoichiometrically  with  proteins  if  the  hydrogen  ion 
concentration  is  properly  taken  into  consideration. 

Similar  experiments  were  made  with  casein  prepared  after  the 
method  of  L.  L.  Van  Slyke  and  J.  C.  Baker,1  who  described  in 

1  VAN  SLYKE,  L.  L.  and  BAKER,  J.  C.,  J.  Biol  Chem.,  vol.  35,  p.  127, 
1918. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          53 

1918  a  method  for  preparing  "pure  casein"  from  skimmed  milk, 
which  consisted 

"in  the  gradual  addition  of  acid  and  its  immediate  distribution  through 
the  mass  of  milk  without  causing  coagulation  of  casein  at  the  point 
where  the  acid  first  comes  into  contact  with  a  portion  of  the  milk. 
This  result  can  be  accomplished  by  introducing  the  acid  below  the 
surface  of  the  milk  with  high-speed  mechanical  stirring.  After  stand- 
ing under  gentle  stirring  for  3  hours  with  acidity  just  below  the  point  of 
casein  coagulation,  addition  of  acid  is  continued  slowly,  accompanied 
as  before  by  rapid  stirring  in  order  to  obtain  the  particles  of  casein 
coagulum  in  the  finest  possible  state  of  division." 

The  coagulated  casein  is  then  centrifuged  and  after  repeated 
washings  is  found  free  from  Ca  and  inorganic  P.  As  Van  Slyke 
and  Baker  point  out,  the  pH  of  this  casein  coagulum  is  about 
4.5  to  4.6,  i.e.,  it  is  slightly  below  the  isoelectric  point.  The 
essential  feature  of  Van  Slyke  and  Baker's  method  therefore 
consists  in  slowly  bringing  the  milk  or  casein  solution  approxi- 
mately to  the  pH  of  the  isoelectric  point  of  casein.  The  writer 
has  shown  that  gelatin  gives  off  all  ionogenic  impurities  at  the 
isoelectric  point  and  Van  Slyke  and  Baker's  experiments  show 
that  the  same  method  works  also  with  casein.  The  casein 
prepared  after  Van  Slyke  and  Baker's  method  is  also  free  from 
albumin  since  this  latter  protein  is  soluble  at  pH  4.5  or  4.7, 
and  is,  hence,  removed  from  the  insoluble  isoelectric  casein  by 
washing. 

In  our  experiments1  we  used  casein  prepared  after  Van  Slyke 
and  Baker's  method  from  skimmed  milk  and  in  addition  from  a 
"pure  casein"  of  the  market.  Both  preparations  gave  practi- 
cally the  same  result.  In  order  to  remove  traces  of  fat  from  the 
casein  the  latter  was  washed  in  acetone. 

It  is  not  possible  to  prepare  1  per  cent  casein  solutions,  except 
with  a  few  acids,  on  account  of  the  low  solubility  of  the  casein 
salts  with  acids.  It  is,  however,  possible  to  compare  casein 
chloride  and  casein  phosphate  in  1  per  cent  solutions.  One  gram 
of  isoelectric  casein,  prepared  after  Van  Slyke  and  Baker,  was  put 
into  100  c.c.  of  watery  solution  containing  1,  2,  3,  etc.,  c.c.  of 
0.1  N  HC1  or  0.1  N  H3PO4.  The  pH  of  the  casein  solution  was 
,  J.,  J.  Gen.  PhysioL,  vol.  3,  547,  1920-21. 


54 


THEORY  OF  COLLOIDAL  BEHAVIOR 


ascertained  potentiometrically  and  the  number  of  cubic  centi- 
meters of  0.1  N  acid  required  to  bring  the  1  per  cent  casein  solu- 


C 
'3 

a 

o 


i 

.3 

o 

CO 


o 
u 
o 
o 


B 


u 


40 
38 
36 
34 
32 
30 
28 
26 
24 
22 
20 
18 
16 
14 
12 
10 
8 
6 
4 
2 


\ 


\ 


\ 


pH  1.4    1.6   1.8  2.0  2.2  24  2.6   2.8  3.0  3.2   34  3.6  3.8 

FIG.  9. — Ordinates  represent  the  c.c.  of  0.1  N  HC1  or  H3PO4  in  100  c.c.  of  1 
per  cent  casein  solution.  The  abscissa  are  the  pH  of  the  solution.  Approxi- 
mately three  times  as  many  c.c.  of  0.1  N  HsPC^  as  of  0.1  N  HC1  are  required  to 
bring  1  gm.  of  casein  to  the  same  pH. 

tion  to  the  same  pH  were  plotted  over  the  final  pH  of  the  casein 
solution  as  abscissae.  The  casein  chloride  or  casein  phosphate  is 
not  completely  soluble  in  a  1  per  cent  solution  until  the  pH  is 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT  55 

about  3.0  or  a  trifle  below.  When  too  much  acid  is  added,  i.e., 
when  the  pH  is  1.6  or  possibly  a  little  above,  casein  precipitates 
out  again  from  a  1  per  cent  solution. 

Figure  9  gives  the  titration  curves  for  HC1  and  H3PO4,  drawn 
out  within  those  limits  of  pH  within  which  the  casein  salts  are 
soluble  in  a  1  per  cent  solution.  The  curves  show  that- about 
three  times  as  many  cubic  centimeters  of  0.1  N  H3PO4  as  of 
0.1  N  HC1  are  required  to  bring  1  gm.  of  originally  isoelectric 
casein  in  a  1  per  cent  solution  to  the  same  pH;  or  in  other  words, 
H3PO4  combines  with  casein  in  molecular  proportions,  as  should 
be  expected  if  casein  phosphate  is  a  true  chemical  compound. 

It  was  not  possible  to  plot  the  corresponding  curves  for  casein 
sulphate  and  casein  oxalate  since  these  salts  are  too  sparingly 
soluble.  This  is  true  also  for  casein  salts  with  other  acids,  e.g., 
trichloracetic  acid. 

From  all  these  experiments  we  draw  the  conclusion  that  acids 
combine  with  crystalline  egg  albumin,  gelatin,  and  casein  (and 
probably  proteins  in  general)  by  the  same  forces  of-  primary 
valency  by  which  the  same  acids  combine  also  with  crystalloidal 
substances,  e.g.,  NH3  or  NaOH. 

3.  In  the  preceding  experiments  we  started  with  isoelectric 
protein  and  determined  the  number  of  cubic  centimeters  of 
0.1  N  acid  required  to  bring  the  protein  solution  to  a  definite 
pH.  It  seemed  of  interest  to  confirm  our  results  by  the  reverse 
titration;  namely,  by  starting  with  a  protein-acid  salt  of  a 
definite  pH  and  determining  how  many  cubic  centimeters  of 
0.1  N  NaOH  are  required  to  bring  a  solution  of  a  protein-acid  salt 
to  a  definite  pH,  e.g.,  7.0.  This  method  requires,  however,  cer- 
tain corrections  which  will  become  clear  from  the  following  con- 
siderations. The  experiments  were  made  with  gelatin  solutions 
containing  about  0.8  gm.  of  originally  isoelectric  gelatin  in  100  c.c. 
solution.  When  we  add  different  quantities  of  0.1  N  acid,  e.g., 
HBr,  to  0.8  gm.  of  isoelectric  gelatin,  melt,  and  make  a  0.8  per 
cent  solution  by  adding  enough  water  to  bring  the  volume  to 
100  c.c.,  there  is  in  solution  a  mixture  of  two  substances,  namely, 
free  hydrobromic  acid  and  gelatin  bromide.  The  total  amount 
of  Br  contained  in  10  c.c.  solution  can  be  determined  by  titrating 
for  Br;  part  of  this  Br  is  in  combination  with  protein  and  part  is 
in  combination  in  the  free  HBr,  The  latter  part  can  be 


56  THEORY  OF  COLLOIDAL  BEHAVIOR 

ascertained  from  the  pH  of  the  gelatin  bromide  solution  by 
preparing  a  solution  of  HBr  of  the  same  pH  in  water,  without 
gelatin,  and  determining  the  amount  of  Br  in  this  solution  free 
from  gelatin.  By  deducting  this  value  from  the  total  Br  it  can 
be  found  how  much  HBr  is  combined  with  the  gelatin.  Table 
IV  gives  the  results  of  such  an  experiment.1  Row  1  gives  the 
number  of  cubic  centimeters  of  0.01  N  free  hydrobromic  acid 
originally  contained  in  100  c.c.  of  the  0.8  per  cent  solution  of  orig- 
inally isoelectric  gelatin.  Row  2  gives  the  pH  of  each  gelatin- 
bromide  solution  after  equilibrium  is  established ;  Row  3  the  total 
amount  of  0.01  N  Br  found  in  10  c.c.  of  the  solution;  and  Row 

4  gives  the  amount  of  Br  actually  in  combination  with  gelatin 
after  deducting  the  amount  of  Br  in  the  free  HBr  (not  in  com- 
bination with  gelatin)  from  the  total  amount  of  Br  found. 

There  is  a  second  method  of  ascertaining  the  amount  of  HBr  in 
combination  with  a  given  mass  of  gelatin,  namely  by  titrating  for 
acid  with  NaOH.1  In  this  case  the  number  of  cubic  centimeters 
0.01  N  NaOH  required  to  bring  10  c.c.  of  the  gelatin-bromide 
solution  to  a  pH  of  7.0  must  be  determined.  This  gives  the 
total  acid,  from  which  the  value  for  free  acid  not  in  combination 
with  gelatin  is  to  be  deducted.  This  value  is  obtained  by  titrat- 
ing a  solution  of  HBr  (free  from  gelatin)  of  the  same  pH  as  the 
gelatin-bromide  solution  with  NaOH.  A  second  correction, 
however,  must  be  made ;  namely,  the  quantity  of  NaOH  required 
to  bring  10  c.c.  of  an  0.8  per  cent  solution  of  isoelectric  gelatin  to  a 
pH  of  7.0  must  be  ascertained.  This  value  was  found  to  be  about 
1.8  c.c.  0.01  NaOH  for  lOc.c.  of  a  0.8  per  cent  solution  of  isoelectric 
gelatin.  This  value  must  also  be  deducted,  and  if  these  two 
deductions  are  made,  approximately  the  same  figures  are  reached 
as  by  direct  titration  for  Br.  This  is  shown  by  Table  IV.  Row 

5  gives  the  number  of  cubic  centimeters  0.01  N  NaOH  required  to 
bring  10  c.c.  of  gelatin  solution  to  pH  of  7.0.     Row  6  gives  the 
corrected    NaOH   values,    i.e.,    after   the   two  deductions  just 
mentioned  are  made  from  the  values  in  Row  5.     A  comparison 
of  the  values  of  Row  6  with  those  of  Row  4  shows  that  they  are 
identical  within  the  limits  of  the  accuracy  of  our  methods. 

This  method  of  titrating  with  NaOH  allows  us,  therefore,  to 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  1,  p.  559,  1918-19. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          57 


o 

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1.  Cubic  centimeters  0.01  N  HBr  added  
2.  pH  of  gelatin  solution  
3.  Cubic  centimeters  0.01  N  Br  found  in  10  c.c.  of 
gelatin  solution  
4.  Corrected  values  of  Br  
5.  Cubic  centimeters  0.01  N  NaOH  required  to 
bring  10  c.c.  of  gelatin  solution  to  pH  7.0  .. 
6.  Corrected  NaOH  value  

(In  this  experiment  the  collodion  bag 
same  concentration  as  that  added  to 
solution  so  that  at  equilibrium  the  latte 

58 


THEORY  OF  COLLOIDAL  BEHAVIOR 


find  out  the  amount  of  any  acid  in  combination  with  a  given  mass 
of  gelatin  of  a  certain  pH. 

With  the  new  method  we  can  also  confirm  the  statement  that 
weaker  dibasic  or  tribasic  acids,  like  oxalic  or  phosphoric,  com- 
bine with  gelatin  in  molecular  proportions.  Table  V  gives  the 
equivalents  of  HNO3,  oxalic,  and  phosphoric  acids  in  combination 
with  gelatin  at  different  pH  in  10  c.c.  of  0.8  per  cent  solution  of 
originally  isoelectric  gelatin. 

The  values  found  for  HNO3  in  Table  V  are  slightly  less  than 
those  found  for  HBr  in  Table  IV  and  HC1,  due  to  the  fact  that 
the  concentration  of  gelatin  was  slightly  less  in  the  experiments 
recorded  in  Table  V  than  in  Table  IV.1  A  comparison  of  the 
figures  for  NaOH  values  for  HNO3,  and  for  the  PO4  values  (Table 
V,  Rows  1  and  3),  found  by  direct  titration  for  PO4  with  the  uranyl- 
acetate  method,  shows  for  the  two  values  practically  the  ratio  of 
1 : 3  at  the  same  pH;  i.e.,  three  times  as  much  H3P04  as  HNO3  is  in 
combination  with  the  same  mass  of  gelatin.  The  figures  for 
HNO3  and  oxalic  acid  (Rows  1  and  2,  Table  IV)  give  the  ratio  of 
approximately  1:2  for  pH  3.5  or  below.  Hence,  oxalic  and  phos- 
phoric acids  combine  in  molecular  proportions  with  gelatin.  In 
the  same  way  it  was  shown  that  H2S04  combines  in  equivalent 
proportions  with  gelatin, 

These  measurements  confirm  the  conclusions  at  which  we 
arrived  by  the  other  method. 

TABLE  V.— CUBIC  CENTIMETERS  OF  0.01  N  ACID  IN  COMBINATION  WITH 

GELATIN  IN   10  c.c.  OF  AN  0.8  PER  CENT  GELATIN  SOLUTION  AT 

DIFFERENT  pH 


pH 

3.1 

3.2 

3.3 

3.4 

3.5 

3.7 

3.9 

4.1 

4.2 

4.3 

1.  HNO3 

4.35 
9.6 

4.1 
8.75 
12.4 

3.6 
7.6 
10.4 

3.2 
6.7 

9.8 

2.85 
6.00 
9.00 

2.45 
4.3 

7.4 

1.9 
3.0 

5.8 

1.45 
4.5 

1.65 
2.6 

0.75 
2.1 

2.  Oxalic  acid  

3.  H3PO4  

1  In  these  earlier  experiments  1  gm.  of  powdered  gelatin  was  brought  to 
the  isoelectric  point.  This  entailed  some  loss,  especially  during  the  wash- 
ing, which  varied  slightly  in  different  experiments.  In  later  experiments 
this  source  of  error  was  avoided  by  using  a  stock  solution  of  about  8  per 
cent  isoelectric  gelatin  and  ascertaining  the  concentration  of  isoelectric 
gelatin  by  dry-weight  determinations. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT 


59 


It  was  found  in  these  experiments  that  all  strong  monobasic 
acids,  like  HBr  or  HNO3,  gave  the  same  titration  curve  as  HC1. 
This,  however,  was,  of  course,  no  longer  the  case  for  weak  acids. 
The  weaker  the  acid  the  more  is  required  to  bring  the  protein 
solution  to  the  same  pH.  This  is  illustrated  in  Fig.  10,  which 
gives  the  titration  curves  for  0.1  N  acetic,  mono-,  di-,  and  tri- 


3 


22 


£6    28  3.0    32  3.4  3.6  3.8  40  42  44  46  48 


FIG.  10. — The  ordinates  represent  the  number  of  c.c.  of  0.1  N  acetic,  mono-, 
di-,  and  trichloracetic  acids  required  to  bring  about  0.8  gm.  of  isoelectric  gelatin 
to  the  pH  indicated  by  the  abscissae.  Enough  HoO  was  added  to  bring  the 
gelatin-acid  solution  to  a  volume  of  100  c.c. 


chloracetic  acids  with  the  same  mass  of  isoelectric  gelatin  (about 
0.8  gm.)  in  100  c.c.  solution.  It  is  obvious  that  the  weaker  the 
acid  the  more  is  required  to  bring  the  same  mass  of  isoelectric 
gelatin  to  the  same  pH. 

On  account  of  the  enormous  quantities  required  in  the  case  of 
weak  acids,  it  is  not  well  possible  to  plot  the  quantity  of  acid  in 
combination  with  a  given  mass  of  protein  in  the  same  way  as  done 
in  the  case  of  HC1 ;  but  it  will  be  shown  in  the  next  chapter  by  an 
indirect  method  that  the  amount  of  anion  combined  with  a  given 


60 


THEORY  OF  COLLOIDAL  BEHAVIOR 


m^-     ,x  protein  in  the  same  volume  of  solution  is  the  same  for  a 
given  pH  no  matter  whether  the  acid  is  strong  or  weak. 

4.  If  the  numbers  of  cubic  centimeters  of  0.1  N  KOH,  NaOH, 
Ca(OH)2,  and  Ba(OH)2  are  measured  which  must  be  contained 


10 


11 


FIG.  11. — Curves  representing  the  number  of  c.c.  of  0.1  N  NH4OH,  NaOH, 
and  Ca(OH)2  required  to  bring  1  gm.  of  isoelectric,  crystalline  egg  albumin  in 
100  c.c.  solution  to  different  pH.  The  curves  for  NaOH  and  Ca(OH)2  are 
identical. 

in  100  c.c.  of  a  1  per  cent  solution  of  originally  isoelectric  crystalline 
egg  albumin  to  bring  the  solution  to  the  same  pH,  it  is  found  that 
these  numbers  are  identical  and  that  the  values  for  the  four  bases 
lie  in  one  curve.  This  means  that  Ca  (OH)  2  and  Ba  (OH)  2  combine 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT 


61 


in  equivalent  proportions  with  crystalline  egg  albumin;  i.e., 
combine  with  crystalline  egg  albumin  in  the  same  stoichiome- 


40 
38 
36 


52  32 

<D 

u  30 

o~  28 

0  26 


22 


u 

CD 


u 
0 


20 
18 
16 

14 
12 

10 

8 
6 

4 


Na 


Cd 

-Kr 


Ba 


casemate 


71 


pH    6 


8 


10 


11 


12 


FIG.  12.— Ordinates  are  the  c.c.  of  0.1  N  NaOH,  KOH,  Ca(OH)2,  and  Ba(OH)2 
in  100  c.c.  of  1  per  cent  solution  of  casein.  Abscissae  are  the  pH  of  the  solution. 
The  curves  for  the  four  alkalies  are  identical,  proving  that  Ba  and  Ca  combine 
with  casein  in  equivalent  proportion. 

trical  way  in  which  they  combine  with  crystalloidal  acids. 
This  is  equally  true  for  the  combination  of  these  bases  with 
isoelectric  albumin  (Fig.  11),  with  casein  (Fig.  12),  and  with 


62 


THEORY  OF  COLLOIDAL  BEHAVIOR 


gelatin  (Fig.  13).    In  this  latter  case  the  solution  contained  only 
about  0.8  gm.  of  originally  isoelectric  gelatin  in  100  cc.  solution.1 


q 


e 


<&- 

1 

8 
^ 

8 


0.1N 


0.1N 


o.iNBaio: 


Nate 


KOH 


and 


01N 


:a(ort) 


/ 


67    72    7.7   82    87    92    97  10.2  107  112  11.7 


3  DH47  5.2    5.7    62 

8 

FIG.  13.—  Curves  for  the  number  of  c.c.  of  0.1  N  NaOH,  KOH,  Ba(OH)2, 
and  Ca(OH)2  required  to  bring  the  same  mass  of  about  0.8  gm.  of  isoelectric 
gelatin  in  100  c.c.  solution  to  different  pH.  All  four  curves  are  identical. 

The  question  may  be  finally  raised,  How  many  molecules  of 
acid  or  alkali  can  combine  with  one  molecule  of  protein?  The 
smoothness  of  the  titration  curves  of  isoelectric  proteins  with 
acids  indicates  that  either  only  one  or  many  molecules  of  a 
monobasic  acid,  e.g.,  HC1,  combine  with  one  molecule  of  protein, 
since  otherwise,  the  curves  could  not  be  smooth.  It  is  not 
probable  that  only  one  molecule  of  acid  combines  with  one  mole- 
cule of  protein. 

Procter  and  Wilson,  have  reached  the  conclusion  that  the 
equivalent  weight  of  gelatin  is  768  (see  Chap.  XI),  and  Wintgen 
and  Kruger2  give  the  value  as  839.  According  to  the  recent 


,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  85,  1920-21. 
2  WINTGEN,  R.,  and  KRUGER,  K.,  Kolloid-Z.,  vol.  28,  p.  81,  1921. 


CORRECTNESS  OF  THE  CHEMICAL  VIEWPOINT          63 

analyses  by  Dakin,1  gelatin  contains  1.4  per  cent  phenylalanme, 
which  would  give  as  the  minimal  molecular  weight  of  gelatin 
11,800.  Procter  and  Wilson's  value  leads  to  the  result  that 
about  15,  or  a  multiple  of  15,  molecules  of  a  monobasic  acid 
combine  with  one  molecule  of  gelatin. 

It  can  be  stated,  as  the  result  of  all  these  titration  experiments, 
that  the  ratios  in  which  acids  and  bases  combine  with  proteins 
are  identical  with  the  ratios  in  which  acids  and  bases  combine 
with  crystalloids.  Or,  in  other  words,  the  forces  by  which 
gelatin,  egg  albumin,  and  casein  (and  probably  proteins  in 
general)  combine  with  acids  or  alkalies  are  the  purely  chemical 
forces  of  primary  valency. 

The  question  may  be  raised,  How  can  the  fact  that  proteins 
combine  stoichiometrically  be  reconciled  with  the  statement  that 
their  solutions  frequently  contain  aggregates  of  molecules? 
This  latter  fact  led  to  the  assumption  of  adsorption  at  the  surface 
of  each  micella,  but  without  cogent  reason.  The  protein  micellae 
which  may  exist  in  a  solution  of  gelatin  in  water  are  not  compar- 
able with  metallic  spheres  or  oil  globules  in  water,  where  the  two 
phases  are  separated  by  a  continuous  boundary.  When  a  1  per 
cent  gelatin  solution  sets  to  a  gel,  the  equal  distribution  of  the 
molecules  of  the  gel  in  the  water  remains  the  same.  The  random 
orientation  of  the  gelatin  molecules  in  the  solution  may  change  to 
a  more  definite  orientation  in  the  gel,  but  the  average  distance 
between  the  protein  molecules  will  probably  not  change.  The 
interstices  between  the  molecules  remain  the  same,  and  the 
protein  molecules  and  protein  ions  remain  as  accessible  to  alkali 
or  acid  in  the  gel  as  are  molecules  or  ions  in  true  solution.  The 
micellae  of  gelatin  in  solution  are  submicroscopic  particles  of  jelly 
and  there  is  no  reason  why  the  reactions  between  gelatin  and 
electrolytes  should  not  be  stoichiometrical  even  if  the  protein 
were  entirely  in  the  gel  state. 

The  titration  experiments  given  in  this  chapter  show  also  why 
it  is  necessary  to  compare  the  relative  efficiency  of  two  kinds  of 
ions  of  the  same  sign  not  only  for  the  same  concentration  of  the 
originally  isoelectric  protein  but  also  for  the  same  pH.  As  the 
combination  curves  Figs.  6  and  8  show,  at  each  pH  only  part  of 
the  mass  of  the  protein  present  exists  in  the  form  of  a  salt,  the 

1  DAKIN,  H.  D.,  J.  BioL  Chem.,  vol.  44,  p.  499,  1920. 


64  THEORY  OF  COLLOIDAL  BEHAVIOR 

rest  exists  as  non-ionogenic  protein.  Only  if  enough  acid  (or 
alkali)  is  added,  is  all  the  protein  transformed  into  a  salt.  The 
combination  curves  show  that  at  the  same  pH  the  same  fraction 
of  the  protein  present  exists  in  the  form  of  a  protein  salt.  If  it  is 
desired  to  compare  the  relative  efficiency  of  different  ions  in 
combination  with  a  protein,  one  must  be  sure  that  the  concen- 
tration of  originally  isoelectric  protein  is  the  same  in  both  solu- 
tions and  that  the  fraction  of  protein  which  has  combined  with 
the  two  ions  is  the  same.  This  is  only  true  when  the  solutions  of 
the  protein  salts  to  be  compared  have  not  only  the  same  concen- 
tration of  originally  isoelectric  protein  but  also  the  same  pH. 

There  existed  no  reason  for  comparing  the  effects  of  different 
ions  at  the  same  pH  as  long  as  the  titration  curves  given  in  this 
chapter  were  not  known.  But  the  knowledge  of  these  curves 
forces  the  experimenter  to  change  his  methods  and  to  base  all  the 
comparisons  of  the  influence  of  ions  on  the  physical  prop- 
erties of  proteins  on  protein  solutions  of  equal  hydrogen  ion 
concentrations. 


CHAPTER  V 
THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES 

(A)  OSMOTIC  PRESSURE 

In  this  chapter  it  will  be  shown  that  the  combining  ratios  of 
acids  and  alkalies  with  proteins  furnish  the  key  for  the  under- 
standing of  the  influence  of  ions  on  the  physical  properties  of 
proteins,  inasmuch  as  only  the  sign  of  charge  and  the  valency 
but  not  the  other  properties  of  an  ion  influence  such  physical 
qualities  of  proteins  as  osmotic  pressure,  viscosity,  and,  in  the 
case  of  gelatin,  swelling.  In  this  discussion  only  the  monovalent 
and  bivalent  ions  will  be  considered. 

The  fact  to  be  proved  is  contrary  to  the  statements  current  in 
colloid  chemistry  according  to  which  the  chemical  nature  of  the 
ion  is  of  as  much  importance  as  the  valency.  As  already  stated 
in  the  first  chapter,  the  ions  have  been  arranged  in  series, 
the  so-called  Hofmeister  series,  according  to  their  relative  in- 
fluence on  swelling,  viscosity,  and  osmotic  pressure  of  proteins. 
It  is  perfectly  true  that  the  different  ions  of  the  same  valency, 
e.g.,  Li,  Na,  K,  Rb,  Cs,  or  Cl,  Br,  and  I,  have  different  chemical 
properties  according  to  their  position  in  the  periodic  table,  and 
monovalent  anions,  such  as  NO3,  CH3COO,  also  have  definite 
chemical  characteristics  different  from  those  of  I  or  Br  or  Cl. 
These  differences  manifest  themselves  in  many  phenomena, 
e.g.,  in  solubility,  but  they  are  obviously  of  minor  importance 
in  their  influence  on  the  physical  properties  of  proteins  alluded 
to,  for  a  reason  which  will  become  clear  in  the  second  part  of  the 
book.  For  the  present  it  will  only  be  shown  that  the  Hofmeister 
ion  series  are  largely  the  result  of  the  same  methodical  error 
which  had  prevented  the  recognition  of  the  fact  that  acids  and 
alkalies  combine  with  proteins  stoichiometrically,  namely,  the 
failure  to  measure  the  hydrogen  ion  concentration  of  the  protein 
solutions.  If  we  wish  to  compare  the  relative  efficiency  of  two 
5  65 


66  THEORY  OF  COLLOIDAL  BEHAVIOR 

ions,  e.g.,  Cl  and  CH3COO,  on  the  osmotic  pressure  or  viscosity 
of  protein  solutions,  it  is  absolutely  necessary  to  do  so  at  the 
same  pH  and  the  same  concentration  of  originally  isoelectric 
protein.  If  this  is  done,  it  will  be  found  that  the  Hofmeister 
series  have  practically  no  real  significance  and  that  essentially 
only  the  valency,  not  the  specific  nature  of  the  ion  in  combination 
with  the  protein,  influences  its  physical  properties. 

In  the  preceding  chapter  it  was  seen  that  at  the  same  pH  three 
times  as  many  cubic  centimeters  of  0.1  N  H3PO4  as  of  HNOsare  in 
combination  with  1  gm.  of  originally  isoelectric  gelatin  in  100  c.c. 
of  solution.  From  this  it  follows  that  the  anion  of  gelatin  phos- 
phate is  the  monovalent  ion  H2PO4  and  not  the  trivalent  anion 
P04.  It  follows  likewise  from  the  combining  ratios  discussed  in 
Chap.  IV  that  the  anion  of  oxalic  acid  in  combination  with 
protein  below  pH  =  3.0  is  the  monovalent  anion  HC2O4,  while  at 
pH  above  3.0  the  oxalic  acid  dissociates  to  an  increasing  degree  as 
a  dibasic  acid,  forming  a  divalent  anion  C2O4  with  protein.  The 
same  must  be  true,  mutatis  mutandis,  for  all  weak  dibasic  or 
tribasic  acids,  e.g.,  citric,  tartaric,  or  succinic  acids,  namely,  that 
at  pH  below  4.7  they  form  protein  salts  with  chiefly  monovalent 
anions.  It  follows  also  from  the  combining  ratios,  that  the  salt 
of  a  protein  with  a  strong  dibasic  acid,  as  H2SO4,  must  have  a 
divalent  anion,  e.g.,  SO4.  On  the  basis  of  our  valency  rule,  we 
should,  therefore,  expect  that  the  osmotic  pressure  of  1  per  cent 
solutions  of  originally  isoelectric  gelatin  with  different  acids  of 
the  same  pH  should  be  identical  for  all  gelatin  salts  with  monova- 
lent anion;  in  other  words,  1  per  cent  solutions  of  gelatin  chloride, 
bromide,  nitrate,  tartrate,  succinate,  citrate,  or  phosphate  should 
all  have  about  the  same  osmotic  pressure  and  the  same  viscosity 
at  the  same  pH;  and  the  same  should  be  true  for  swelling;  while 
gelatin  sulphate,  which  has  a  bivalent  anion,  should  have  a  much 
lower  osmotic  pressure,  viscosity,  or  swelling.  We  will  show 
first  that  this  is  true  for  the  osmotic  pressure  of  protein  solutions. 

The  simple  method  of  R.  S.  Lillie1  was  employed  for  the  measure- 
ment of  the  osmotic  pressure  of  gelatin  solutions.  Collodion 
bags  of  a  volume  of  about  50  c.c.  were  cast  in  Erlenmeyer  flasks 
assuming  the  shape  of  the  latter.  These  were  prepared  in  a 
uniform  way,  as  follows:  Collodion  (Merck,  275  grains  of  ether 

1  LILLIE,  R.  S.,  Am.  J.  PhysioL,  vol.  20,  p.  127,  1907-08. 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    67 

per  ounce;  27  per  cent  alcohol,  U.  S.  P.  IX)  was  used.  Erlen- 
meyer  flasks  of  a  volume  of  about  50  c.c.  were  rinsed  with  95  per 
cent  alcohol  and  then  filled  to  the  neck  with  the  collodion  solution. 
After  the  flask  was  filled  with  collodion,  the  latter  was  allowed  to 
pour  out  slowly  from  the  flask  which  was  rotated  slowly  by  hand 
during  this  process.  The  process  of  rotating  the  flask  and  pour- 
ing out  the  collodion  was  timed  to  occupy  exactly  2  minutes. 
Then  the  Erlenmeyer  flask,  which  was  now  empty  except  for  a 
film  of  collodion  adhering  to  the  inside  of  the  glass  wall,  was 
allowed  to  dry  for  exactly  2  minutes  at  room  temperature.  It 
was  then  put  under  the  faucet  and  tap  water  was  allowed  to  run 
in  in  a  gentle  stream  for  5  minutes.  The  collodion  film  formed 
inside  the  flask  could  be  pulled  out  being  an  exact  cast  of  the  flask. 
These  collodion  bags  were  closed,  with  the  aid  of  rubber  bands, 
by  a  conical  rubber  stopper  which  was  perforated  to  allow  a  glass 
tube  to  be  pushed  through.  The  collodion  bag  was  filled  with  the 
solution  of  protein  with  the  aid  of  a  small  funnel,  all  air  bubbles 
were  removed  and  the  glass  tube  was  pushed  into  the  bag  to  serve  as 
a  manometer.  The  bag  was  then  put  into  a  beaker  usually  con- 
taining 350  c.c.  of  water,  having  the  same  pH  as  the  protein  solu- 
tion. The  surface  of  the  stopper  was  so  adjusted  that  it  lay  in  the 
surface  of  the  water  in  the  beaker  and  the  glass  tube  (or  manometer) 
was  pushed  a  little  deeper  into  the  bag  so  that  at  the  beginning  the 
level  of  the  protein  solution  was  about  from  20  to  30  mm.  above 
that  of  the  water  in  the  outside  beaker. 

The  water  diffused  from  the  outside  beaker  into  the  protein 
solution  and  the  column  of  liquid  in  the  manometer  rose  to  a 
maximum  which  was  usually  reached  in  about  6  hours  or  possibly 
less.  It  must  be  taken  into  consideration  that  two  changes  in 
pH  will  occur  in  these  experiments  which  affect  the  osmotic 
equilibrium.  The  one  change  is  due  to  the  Donnan  equilibrium 
which  was  referred  to  in  the  introduction.  The  other  change  is 
due  to  the  influence  of  the  CO2  of  the  air  in  the  outside  solution 
and  this  influence  is  especially  disturbing  when  alkaline  'solutions 
are  used.  It  must  also  be  borne  in  mind  that  in  these  experi- 
ments the  protein  solution  is  also  usually  diluted  through  the 
entrance  of  water  into  the  collodion  bag.  In  later  chapters 
measures  will  be  mentioned  by  which  these  sources  of  error 
can  be  avoided  or  diminished. 


68 


THEORY  OF  COLLOIDAL  BEHAVIOR 


One  per  cent  solutions  of  originally  isoelectric  protein  were 
made,  each  solution  containing  a  certain  amount  of  an  acid  or  of 
alkali  to  give  it  a  definite  pH.  In  each  case  the  collodion  bag 


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FIG.  14. — Influence  of  pH  and  valency  of  anion  on  osmotic  pressure  of  solu- 
tions of  different  gelatin-acid  salts.  The  osmotic  pressure  is  a  minimum  at  the 
isoelectric  point,  pH  4.7,  rises  with  the  addition  of  acid  until  pH  is  3.4,  and 
then  drops  .upon  the  addition  of  more  acid.  The  curves  for  gelatin  chloride  and 
gelatin  phosphate  are  identical. 

containing  the  gelatin  solution  was  dipped,  as  described,  into  a 
beaker  containing  350  c.c.  of  water  of  originally  the  same  pH  as 
that  of  the  protein  solution  used.  On  account  of  the  Donnan 
equilibrium  this  equality  of  pH  in  the  inside  and  outside  solu- 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    69 

tions  was  not  retained,  the  pH  rising  higher  inside  than  outside  in 
the  case  of  solutions  of  gelatin-acid  salts.  The  observations 
lasted  usually  for  1  day  but  the  level  of  liquid  in  each  manometer 
was  recorded  at  first  every  20  or  30  minutes  and  the  values 
recorded  the  next  day  were  used  to  plot  the  curves  in  Fig.  14. 
The  osmotic  equilibrium  was  usually  established  in  about  6 
hours.  The  experiments  were  carried  on  in  a  thermostat  at  a 
temperature  of  24°C. 

Figure  14  gives  the  curves  of  the  osmotic  pressure  for  solutions 
of  originally  1  per  cent  isoelectric  gelatin  with  four  different 
acids,  HC1,  H2S04,  oxalic,  and  phosphoric  acids.1  The  abscissae 
are  the  pH  of  the  gelatin  solutions  after  osmotic  equilibrium  was 
established,  i.e.,  at  the  end  of  the  experiment.  The  pH  was 
always  determined  potentiometrically.  The  reader  will  notice 
that  the  four  curves  have  a  number  of  characteristic  features  in 
common.  The  osmotic  pressure  is,  in  all  cases,  a  minimum  at 
the  isoelectric  point,  namely,  at  pH  =  4.7;  it  rises  with  increasing 
hydrogen  ion  concentration  (or  diminishing  pH) ,  and  the  curves 
all  reach  a  maximum  at  about  pH  =  3.4.  When  the  hydrogen 
ion  concentration  rises  still  further  (or  with  a  further  drop  in  pH) 
the  curves  for  the  osmotic  pressure  of  the  solutions  of  the  four 
gelatin  salts  diminish  almost  as  steeply  as  they  rose  on  the  other 
side  of  the  maximum.  It  may  be  noticed  in  passing,  that  Pauli2 
and  Manabe  and  Matula3  speak  of  a  maximum  in  the  viscosity 
curves  of  albumin  at  a  pH  of  about  2.1.  It  will  be  observed  that 
the  maximum  for  osmotic  pressure  lies  at  a  much  higher  pH, 
namely  at  about  pH  3.4,  and  that  at  pH  2.1  the  curves  are  at  a  low 
level  again,  not  much  above  that  of  the  isoelectric  point.  This 
form  of  the  curves  of  osmotic  pressure  when  plotted  as  a  func- 
tion of  pH  of  the  protein  solutions  is  very  characteristic  and 
invariable. 

The  main  point,  however,  which  interests  us  in  this  connection 
is  the  proof  of  the  valency  rule.  The  titration  curves  show  that 
in  the  case  of  gelatin  phosphate  as  well  as  of  gelatin  chloride  the 
anion  is  monovalent,  H2P04  and  Cl.  The  valency  rule  demands 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  691,  1920-21. 

2  PAULI,  W.,  "  Kolloidchemie  der  Eiweisskorper,"  Dresden  and  Leipsic, 
1920. 

3  MANABE,  K.,  and  MATULA,  J.,  Biochem.  Z.,  vol.  52,  p.  369,  1913. 


70  THEORY  OF  COLLOIDAL  BEHAVIOR 

that  the  osmotic  pressures  of  the  two  salts  should  be  identical 
and  a  glance  at  Fig.  14  shows  that  this  is  the  case.  The  anion 
of  gelatin  oxalate  should  also  be  essentially  monovalent  for  pH 
below  3.0  and  we  see  that  the  descending  branch  of  the  oxalate 
curve,  from  pH  3.0  and  below,  practically  coincides  with  the 
descending  branch  of  the  curve  for  gelatin  chloride  and  phos- 
phate. For  pH  above  3.0  the  curve  for  the  osmotic  pressures  of 
gelatin  oxalate  is  slightly  lower  than  the  curve  for  gelatin  phos- 
phate and  gelatin  chloride,  as  the  theory  of  electrolytic  dissocia- 
tion demands,  since  for  pH  above  3.0  oxalic  acid  dissociates 
electrolytically  more  and  more  like  a  dibasic  acid  the  higher 
the  pH.  Hence,  at  about  pH  3.4  the  majority  of  the  anions  of 
gelatin  oxalate  is  monovalent,  but  a  certain  small  percentage  is 
divalent.  For  this  reason  the  curve  for  gelatin  oxalate  is  at 
pH  3.4  or  for  higher  pH  not  quite  as  high  as  that  for  gelatin 
chloride  or  phosphate.  This  is  in  strict  agreement  with  the 
titration  curves  in  Fig.  7. 

The  titration  curves  in  Fig.  7  show  also  that  H2S04  forms  a 
divalent  anion  in  combining  with  gelatin  and  we  notice  that  the 
maximum  of  the  osmotic  pressure  curve  at  pH  3.4  is  less  than 
one-half  that  of  the  osmotic  pressure  curve  for  gelatin  chloride 
or  gelatin  phosphate  at  the  same  pH. 

These  results  are  then  in  full  agreement  with  the  titration 
experiments  if  we  assume  that  only  (or  chiefly)  the  sign  and  the 
valency  of  the  ion  with  which  the  protein  is  in  solution  determine 
the  osmotic  pressure  of  the  protein  salt  formed,  while  the  nature 
of  the  ion  has  either  no  effect  or  if  it  has  any  effect  the  latter  must 
be  so  small  that  it  escapes  detection. 

If  the  Hofmeister  series  were  correct,  we  should  have  expected 
that  the  curve  for  the  osmotic  pressure  of  gelatin  phosphate 
should  have  been  of  the  order  of  that  of  gelatin  sulphate  or  even 
lower  instead  of  being  equal  to  that  of  gelatin  chloride;  and  the 
same  should  have  been  true  for  the  curve  for  gelatin  oxalate. 

I  have  repeated  these  experiments  so  often  that  there  can  be 
no  doubt  about  the  correctness  of  the  result. 

The  experiments  with  1  per  cent  solutions  of  originally  isoelec- 
tric  crystalline  egg  albumin  confirm  the  valency  rule  also  for 
this  salt.1  The  abscissae  are  again  the  pH  determined  at  the 
,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  85,  1920-21. 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    71 

beginning  of  the  experiment,  the  ordinates  the  osmotic  pressure 
after  equilibrium  was  reached.  The  acids  used  were  HC1,  H2SO4, 
oxalic  acid,  and  H3PO4  (Fig.  15).  The  reader  notices  again  that 
the  osmotic  pressures  are  a  minimum  at  the  isoelectric  point, 
that  they  reach  a  maximum  at  pH  a  little  above  pH  3.2,  and 
that  they  then  drop  again. 


FIG.  15. — Osmotic  pressure  of  different  albumin-acid  salts.  The  ordinates 
indicate  the  osmotic  pressure  (in  mm.  of  1  per  cent  albumin  solution);  the 
abscissae  are  the  pH.  All  solutions  are  1  per  cent  in  regard  to  isoelectric  albumin. 
The  curves  for  albumin  chloride  and  albumin  phosphate  are  identical. 


The  four  curves  confirm  the  valency  rule.  The  curves  for 
albumin  chloride  and  albumin  phosphate  are  practically  identical, 
that  for  albumin  sulphate  is  almost  but  not  quite  half  as  high  as 
that  of  phosphate,  and  the  curve  for  oxalate  is  at  the  maximum 
a  little  lower  than  that  for  chloride. 

The  valency  rule  holds  also  for  casein-acid  salts.1  Since 
casein  oxalate  and  sulphate  are  too  sparingly  soluble  we  can  only 
compare  the  osmotic  pressures  of  casein  phosphate  and  casein 
chloride.  The  curves  for  the  osmotic  pressures  of  these  two 
J.,  J,  Gen.  Physiol,  vol.  3,  p.  547,  1920-21, 


72 


THEORY  OF  COLLOIDAL  BEHAVIOR 


salts  are  alike  if  plotted  over  the  pH,  as  Fig.  16  shows.     The 
maximal  osmotic  pressure  lies  at  pH  of  about  3.0. 

There  is  then  no  doubt  that  the  curves  for  the  osmotic  pressures 
of  the  three  proteins,  gelatin,  crystalline  egg  albumin,  and 
casein  obey  the  valency  rule,  and  show  no  appreciable  influence 
of  the  nature  of  the  ion  except  that  of  the  sign  of  charge  and 
valency. 


FIG.  16. — Osmotic  pressure  of  1  per  cent  solutions  of  casein  chloride  and  casein 
phosphate  as  function  of  pH.     The  two  curves  are  almost  identical. 

In  the  older  experiments  in  which  the  hydrogen  ion  concentra- 
tions were  not  measured,  the  action  of  weak  acids  led  the  investi- 
gators into  error.  In  the  Hofmeister  series  it  is  generally 
contended  that  acetic  acid  acts  like  sulphuric  acid  and  not  like 
hydrochloric  or  nitric  acids.  This  is  due  to  the  fact  that  the 
investigators  compared  the  effects  of  different  acids  at  equal 
molecular  concentrations  instead  of  comparing  the  effects  of 
different  acids  at  the  same  pH.  If  this  is  done  it  is  found  that 
acetic  acid  .acts  like  HC1  and  not  like  H2SO4.  Figure  17  gives 
the  curves  for  the  osmotic  pressure  of  about  0.8  per  cent  solutions 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    73 

of  originally  isoelectric  gelatin  with  six  different  acids,  HC1, 
H2SO4,  acetic,  monochloracetic,  dichloracetic,  and  trichloracetic 
acids  plotted  over  pH  as  abscissae.1  Since  the  concentration  of 


340 
320 
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FIG.  17. — Osmotic  pressure  (in  mm.  BUG)  of  about  0.8  per  cent  solutions  of 
gelatin  chloride,  gelatin  acetate,  monochloracetate,  dichloracetate,  and  tri- 
chloracetate.  The  curves  are  practically  identical. 

the  originally  isoelectric  gelatin  in  these  solutions  was  lower  than 
in  the  experiments  represented  in  Fig.  14  (about  0.8  per  cent 
instead  of  1  per  cent) ,  the  osmotic  pressures  are  also  all  lower,  but 
the  results  are  relatively  the  same.  Thus  the  maximal  osmotic 
1LOEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  85,  1920-21. 


74  THEORY  OF  COLLOIDAL  BEHAVIOR 

pressure  of  gelatin  sulphate  is  in  Fig.  17  also  a  little  less  than  one- 
half  of  the  maximal  osmotic  pressure  of  gelatin  chloride  and  the 
maximum  lies  again  at  pH  of  about  3.4.  The  four  acetic  acids 
have  their  maximum  also  at  the  same  pH  and  this  maximum  is 
equal  to  that  of  HC1.1  The  slight  variations  in  the  height  of  the 
curves  for  the  five  monobasic  acids  are  merely  accidental  and 
probably  chiefly  due  to  slight  differences  in  the  concentration  of 
the  isoelectric  gelatin.  In  these  experiments  each  gram  of 
powdered  gelatin  was  brought  independently  to  the  isoelectric 
point  and  in  this  procedure  about  20  per  cent  of  gelatin  were 
lost,  but  the  loss  varied  slightly  in  the  different  experiments. 
In  the  experiments  represented  in  Fig.  14  a  large  quantity 
of  powdered  gelatin  was  brought  to  the  isoelectric  point  and 
doses  of  1  gm.  of  isoelectric  gelatin  were  used.  In  this  latter 
case  the  quantity  of  originally  isoelectric  gelatin  was  always 
the  same. 

It  was  also  found  that  the  osmotic  pressure  of  0.8  per  cent 
solutions  of  gelatin  tartrate  and  gelatin  citrate  is  approxi- 
mately the  same  as  that  of  gelatin  chloride  of  the  same  pH. 

The  writer  has  also  shown  that  the  curves  for  the  osmotic 
pressure  of  1  per  cent  solutions  of  originally  isoelectric  crystal- 
line egg  albumin  are  identical  for  albumin  chloride,  albumin 
acetate,  and  albumin  dichloracetate,  when  plotted  over  the  pH 
as  abscissae.1 

These  experiments  on  gelatin  and  albumin  leave  no  doubt  that 
the  acetates  behave  like  chlorides  and  not  like  the  sulphates. 
Pauli  claimed  that  trichloracetic  acid  acted  like  sulphuric  acid  but 
this  is  certainly  not  the  case  as  far  as  the  osmotic  pressure  of 
gelatin  solutions  is  concerned. 

The  idea  that  the  valency  of  the  ion  in  combination  with  a 
protein  is  the  chief  if  not  the  only  factor  which  influences  its 
osmotic  pressure  is  corroborated  by  measurements  of  the  osmotic 
pressure  of  metal  gelatinates.  We  had  shown  in  Chap.  IV  that 
Ca(OH)2  and  Ba(OH)2  combine  with  gelatin  in  equivalent  pro- 
portions and  that  hence,  the  ion  in  combination  with  gelatin 
in  these  cases  is  the  bivalent  cation  Ca  or  Ba.  The  experiments 
showed  that  Li,  Na,  K,  and  NH4  gelatinate  have  about  the  same 
,  J.,  J.  Gen.  Physiol.,  vol.  3,  p.  85,  1920-21. 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    75 

osmotic  pressure  at  the  same  pH  and  the  same  concentration  of 
originally  isoelectric  gelatin;  while  under  the  same  conditions  Ba 
and  Ca  gelatinate  have  an  osmotic  pressure  less  than  one-half  of 
that  of  the  metal  gelatinates  with  monovalent  cation.1  The  same 


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FIG.  18. — Curves  of  the  osmotic  pressure  of  NEU,  Na,  and  Ca  albuminate 
at  different  pH.  The  curves  for  NEU  and  Na  albuminate  are  practically 
identical. 

is  true  in  the  case  of  the  metal  salts  of  crystalline  egg  albumin. 
Figure  18  shows  that  the  curves  for  the  osmotic  pressure  of  NH4 
and  Na  albuminate  are  about  the  same  for  the  same  pH  while 
that  for  Ca  albuminate  is  about  half  as  high. 
1  LOEB,  J.,  J.  Gen.  Physiol.,  vol.  3,  p.  85;  547,  1920-21. 


76  THEORY  OF  COLLOIDAL  BEHAVIOR 

Similar  results  were  obtained  in  the  case  of  the  osmotic  pressure 
of  metal  caseinates. 

All  experiments  agree  that  only  the  sign  and  the  valency  of 
the  ion  with  which  a  protein  is  in  combination  determine  its 
osmotic  pressure  while  the  specific  nature  of  the  ion  seems  to 
have  no  influence.  This  fact  is  of  the  greatest  significance  since 
it  was  to  be  expected  if  colloidal  behavior  is  due  to  the  Donnan 
equilibrium.  The  writer  may  state  that  this  valency  rule  was 
found  before  he  was  aware  of  the  fact  that  the  influence  of 
electrolytes  on  the  osmotic  pressure  of  protein  solutions  could  be 
derived  from  the  Donnan  equilibrium. 

(B)  SWELLING 

It  is  generally  stated  in  colloidal  literature  that  solid  blocks 
of  gelatin  swell  more  in  chlorides,  bromides,  or  nitrates  than  in 
water  and  that  they  swell  less  in  citrates,  acetates,  tartrates, 
phosphates,  and  sulphates  than  in  water.  The  author  of  this 
statement  is  Hofmeister1  who  was  a  pioneer  and  who  cannot 
be  blamed  for  not  considering  the  hydrogen  ion  concentration 
of  his  solutions  about  which  nothing  was  known  at  the  time  of 
his  experiments.  In  Hofmeister's  experiments  gelatin  blocks 
were  put  into  salt  solutions  of  a  high  concentration,  and  the 
differences  in  the  effects  observed  in  different  solutions  were  slight. 

He  even  states  that  sugar  solutions  have  a  dehydrating  effect, 
like  certain  salts,  and  this  fact  alone  should  have  warned  chemists 
that  his  experiments  could  not  be  used  for  conclusions  concerning 
the  specific  effects  of  ions  on  the  physical  properties  of  colloids. 
As  far  as  the  writer  knows  the  discrimination  between  "hydrat- 
ing"  and  " dehydrating"  ions  originated  from  these  experiments. 

It  is  often  asserted  that  Hofmeister's  ion  series  for  swelling 
have  been  confirmed  by  other  authors.  Thus  on  page  373  of 
Zsigmondy's  book  "  Kolloidchemie  "  (2nd  edition),  the  following 
statements  are  made  in  support  of  this  impression. 

"Wo.  Ostwald  who  compared  the  efficiency  of  different  acids  found 
that  swelling  diminishes  in  the  acids  in  the  following  order,  HC1  > 
HNOs  >  acetic  acid  >  sulphuric  acid  >  boric  acid.  Fischer  has  shown 
that  the  acid  and  alkali  swelling  of  gelatin  as  well  as  that  of  fibrin  is 

1  HOFMEISTER,  F.,  Arch.  exp.  Path.  u.  Pharm.,  vol.  28,  p.  210,  1891. 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    77 

diminished  by  the  addition  of  salt,  and  that  chlorides,  bromides,  and 
nitrates  have  a  less  dehydrating  action  than  acetates,  sulphates,  or 
citrates.  We  have  here  a  similar  series  as  in  the  case  of  the  precipita- 
tion of  proteins  by  alkali  salts,  although  the  order  does  not  agree 
entirely." 

The  writer  is  inclined  to  interpret  Ostwald's  and  Fischer 's 
experiments  differently  from  Zsigmondy,  since  both  authors 
ignored  the  hydrogen  ion  concentration  of  their  solutions.  Our 
experiments  have  shown  that  it  is  necessary  to  base  conclusions 
concerning  the  relative  efficiency  of  ions  on  experiments  with 
equal  hydrogen  ion  concentration.  By  ignoring  this  postulate 
Ostwald  only  proved  that  acetic  and  boric  are  weaker  acids  than 
nitric  but  not  that  the  acetate  and  borate  anions  have  a  greater 
depressing  effect  on  the  swelling  of  gelatin  than  NO3;  and  Fischer 
only  proved  that  citrates  and  acetates  are  buffer  salts  which 
when  added  to  a  solution  of  a  strong  acid  diminish  its  hydrogen 
ion  concentration,  but  not  that  the  acetate  and  citrate  anions  have 
a  greater  depressing  effect  on  the  swelling  of  gelatin  than  Cl  or 
NO3.  Both  authors  erroneously  ascribed  the  effects  of  variation 
of  pH  to  an  effect  of  the  nature  of  the  anion.  The  Hofmeister 
series  of  ion  effects  on  swelling  has,  in  reality,  never  been 
confirmed. 

If  we  wish  to  study  the  specific  effects  of  ions  on  the  swelling 
of  gelatin  we  must  proceed  from  isoelectric  gelatin,  bringing  it 
to  different  pH  by  different  acids  or  alkalies  and  then  compare 
the  swelling  at  the  same  pH  for  these  different  acids  or  alkalies. 
If  this  is  done  it  is  found  that  when  gelatin  is  in  combination 
with  the  anion  of  a  weak  dibasic  or  tribasic  acid,  e.g.,  tartaric, 
citric,  phosphoric,  its  degree  of  swelling  is  the  same  as  when  it  is  in 
combination  with  Cl  or  NO3;  since  in  all  these  cases  the  anion  of 
the  gelatin  salts  is  monovalent,  and  that  only  in  the  case  of  gela- 
tin sulphate  is  the  swelling  considerably  less,  because  H2SO4  com- 
bines with  gelatin  in  equivalent  and  not  in  molecular  proportions 
as  does  the  weak  dibasic  or  tribasic  acid,  e.g.,  phosphoric.1 

The  following  simple  and  quick  volumetric  method  for  measur- 
ing the  swelling  was  adopted. 

Dry  powdered  gelatin  was  sifted  and  the  grains  no  longer 
going  through  sieve  50  but  going  through  sieve  40  or  30  were 
,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  247,  1920-21. 


78  THEORY  OF  COLLOIDAL  BEHAVIOR 

selected  for  the  experiment.  Doses  of  1  gm.  each  were  weighed 
out  and  each  was  put  for  an  hour  into  100  c.c.  M/128  acetic 
acid  at  10°C.  to  bring  the  gelatin  to  the  isoelectric  point.  The 
powdered  mass  was  then  put  on  a  filter  and  washed  five  times 
with  25  c.c.  of  distilled  water  of  5°C.  In  the  acetic  acid  solution 
and  during  the  washing  on  the  filter  the  powdered  gelatin  is 
stirred  constantly.  In  this  washing  about  20  per  cent  of  the 
gelatin  were  lost,  so  that  the  mass  of  gelatin  in  the  following 
experiments  was  only  about  0.8  gm.  each. 

Each  dose  of  originally  1  gm.  of  dry  powder  which  had  mean- 
while absorbed  a  certain  quantity  of  liquid  (which  was  about  the 
same  for  each  dose  of  isoelectric  powder)  was  then  put  for  1  hour 
at  about  20°  into  100  c.c.  of  different  concentrations  of  the  acid 
or  base  whose  influence  on  swelling  was  to  be  tested,  and  the 
mass  was  frequently  agitated.  To  measure  the  relative  amount 
of  swelling  in  different  acids  or  alkalies  and  at  different  pH  the 
mass  was  poured  into  graduated  cylinders  of  100  c.c.  in  which  the 
granules  settled  very  rapidly  to  the  bottom.  The  cylinders  were 
kept  in  a  water  bath  at  20°  for  about  10  to  15  minutes  and  the 
volume  occupied  by  the  gelatin  granules,  after  settling,  was  then 
read.  This  volume  included  a  certain  amount  of  solution  between 
the  granules  and,  therefore,  the  real  volume  of  the  gelatin  was 
smaller  than  that  read.  While  therefore,  the  method  cannot  be 
used  to  measure  the  absolute  amount  of  swelling  it  allowed  us  to 
determine  the  relative  influence  of  different  acids  or  bases  on  the 
swelling  for  the  same  pH. 

The  pH  inside  the  gelatin  granules  and  the  surrounding 
solution  are  quite  different,  owing  to  the  Donnan  equilibrium. 
It  is,  therefore,  not  correct  to  assume  that  the  pH  of  the  granules 
of  gelatin  is  that  of  the  supernatant  liquid.  The  pH  of  the 
granules  of  gelatin  was  determined  after  the  gelatin  had  been 
poured  on  a  filter  and  the  acid  in  the  interstices  of  the  granules 
of  gelatin  had  been  allowed  to  drain  off.  Traces  of  this  outside 
acid  remained  undoubtedly  at  the  surface  of  the  granules.  •  The 
gelatin  was  then  melted  and  its  volume  brought  to  100  c.c.  by 
adding  enough  distilled  water  of  pH  5.6.  The  pH  was  determined 
potentiometrically.  This  pH  was  probably  a  trifle  too  low  on 
account  of  some  of  the  acid  adhering. 

Figures  19  and  20  give  the  results  of  the  measurements  of  swell- 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES   79 

ing  in  acid.  The  abscissae  are  the  pH  found  in  the  gelatin  after 
equilibrium  was  established.  The  ordinates  represent  the  figures 
for  the  volume  of  the  granules  of  about  0.8  gm.  of  gelatin  in 
different  acids.  It  is  obvious  that  in  all  cases  the  volume  (or 
swelling)  is  a  minimum  at  the  isoelectric  point  pH  =  4.7,  that  it 
rises  with  diminishing  pH  until  the  maximum  is  reached  at  a  pH 
of  about  3.2  or  a  little  less,  and  that  the  curve  drops  steeply  with 


6 


FIG.  19.— Influence  of  HC1,  HNO3,  H3P04,  H2SO4,  trichloracetic,  and  oxalic 
acids  on  the  swelling  of  gelatin.  Abscissae  are  the  pH,  ordinates  the  volume  of 
gelatin.  The  curves  for  all  the  acids  are  practically  identical  except  that  for 
HaSCh  which  is  about  one-half  as  high  as  the  curves  for  the  other  acids. 

a  further  diminution  of  pH  (i.e.,  a  further  increase  of  hydrogen 
ion  concentration) .  The  main  fact  is,  however,  that  the  curves 
for  the  influence  of  HC1,  HNO3,  trichloracecic,  oxalic,  phos- 
phoric, citric,  and  tartaric  acids  are  practically  identical,  proving 
that  only  the  valency  and  not  the  nature  of  the  anion  of  the 
acid  used  influences  the  swelling  of  gelatin;  since  the  anion  of 
weak  dibasic  or  tribasic  organic  acids  combining  with  the  gelatin 
is  always  monovalent. 


80 


THEORY  OF  COLLOIDAL  BEHAVIOR 


The  curve  for  the  swelling  of  gelatin  sulphate,  where  the  anion 
combining  with  gelatin  is  bivalent,  is  only  about  half  as  high  as 
the  curve  for  the  salts  of  gelatin  with  the  anion  of  weak  dibasic 
acids  (Figs.  19  and  20). 


FIG.  20. — Influence  of  citric,  tartaric,  and  acetic  acids  on  swelling  of  gelatin. 
The  curves  for  citric  and  tartaric  acids  are  practically  identical  with  those  for 
HC1  and  HNO3  in  Fig.  19.  That  for  acetic  acid  is  a  little  higher  owing  possibly 
to  some  specific  and  secondary  effect  of  this  acid  on  the  cohesion  of  the  jelly. 

Acetic  acid  gives  an  increasing  amount  of  swelling,  but  it  must 
be  remembered  that  1  M  acetic  acid  had  to  be  used  to  bring  the 
pH  of  the  gelatin  to  3.0,  and  it  is  not  impossible  that  in  this  case 
the  high  concentration  of  undissociated  acid  caused  a  secondary 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES  81 

physical  modification  of  the  gelatin  (e.g.,  diminution  of  cohesion 
between  the  particles  of  gelatin). 

Figure  21  gives  the  curves  for  the  action  of  alkalies  on  swelling. 
The  curves  for  Li,  Na,  K,  and  NH4  gelatinate  of  the  same  pH 
are  practically  the  same,  except  that  the  values  for  NH4OH  are 
irregular  for  pH  above  8.5,  possibly  on  account  of  the  fact  that 
the  concentration  of  NH4OH  required  to  bring  gelatin  to  such  pH 


5  6  7  8  9  10  11  12 

FIG.  21. — Curves  for  the  effect  of  different  bases  on  swelling.  Those  for 
LiOH,  NaOH,  KOH,  and  NH4OH  are  practically  identical  and  about  twice  as 
high  as  those  for  Ca(OH)2  and  Ba(OH)2. 

is  rather  high.  The  main  fact  is  that  the  ratio  of  the  maximal 
swelling  of  gelatin  salts  with  bivalent  cation,  like  Ca  or  Ba,  is 
considerably  less  than  that  of  gelatin  salts  with  monovalent 
cation,  like  Na,  K,  or  NEU.1  This  agrees  with  the  results  of  the 
titration  experiments  which  show  that  Ca(OH)2  and  Ba(OH)2 
combine  with  gelatin  in  equivalent  proportions  and  that,  hence, 
the  cation  in  combination  with  the  gelatin  is,  in  this  case,  bivalent. 

It  should  be  pointed  out  that  the  maximal  swelling  of  gelatin 
in  alkalies  was  less  than  that  in  acids.  This  was  not  observed  in 
the  osmotic  pressure  curves.  It  is  probably  due  to  differences  of 
cohesion  of  the  ions  of  the  gel  in  the  two  cases. 

The  results  show  clearly  that  the  Hofmeister  series  is  not  the 
correct  expression  of  the  relative  effect  of  ions  on  the  swelling  of 

1  LOEB,  J.,  /.  Gen.  PhysioL,  vol.  3,  p.  247,  1920-21. 


82  THEORY  OF  COLLOIDAL  BEHAVIOR 

gelatin,  and  that  it  is  not  true  that  chlorides,  bromides,  and 
nitrates  have  "hydrating"  and  acetates,  tartrates,  citrates,  and 
phosphates  "  dehydrating "  effects.  If  the  pH  of  the  gelatin  is 
taken  into  consideration,  it  is  found  that  for  the  same  pH  the 
effect  on  swelling  is  the  same  for  Cl,  NO3,  trichloracetate,  tartrate, 
succinate,  oxalate,  citrate,  and  phosphate,  while  the  swelling  is 
considerably  less  for  S(>4.  This  is  exactly  what  we  should  expect 
according  to  the  valency  rule  on  the  basis  of  the  combining 
ratios  of  different  acids  with  gelatin,  since  the  weak  dibasic  and 
tribasic  acids  combine  with  gelatin  in  molecular  proportions 
while  the  strong  dibasic  acid  H2SO4  combines  with  gelatin  in 
equivalent  proportions.  In  the  case  of  the  weak  dibasic  acids 
the  anion  in  combination  with  gelatin  is  monovalent  and  in 
the  case  of  the  strong  H2SO4  it  is  bivalent.  Hence,  it  is  only 
the  valency  and  not  the  nature  of  the  ion  in  combination  with 
gelatin  which  affects  the  degree  of  swelling. 

(C)  VISCOSITY 

The  valency  rule  which  permits  us  to  predict  the  relative 
osmotic  pressure  of  solutions  of  protein  holds  also  in  the  case 
of  viscosity  of  gelatin  and  casein  solutions. 

We  will  begin  with  experiments  on  the  influence  of  gelatin 
on  the  viscosity  of  water.1  A  4  per  cent  stock  solution  of 
isoelectric  gelatin  was  prepared,  and  some  of  the  stock  solution 
was  heated  to  45°  and  made  up  to  a  1.6  per  cent  solution  in 
quantity  sufficient  for  a  day's  experiments.  This  1.6  per  cent 
solution  was  kept  during  the  day  at  24°C.  To  50  c.c.  of  this 
solution  was  added  the  desired  acid  or  alkali  in  sufficient  quantity 
and  then  the  volume  raised  to  100  c.c.  by  the  addition  of  enough 
distilled  water.  The  0.8  per  cent  solution  was  then  rapidly 
brought  to  a  temperature  of  45°,  kept  there  for  1  minute  and  was 
then  rapidly  cooled  to  24°C.  The  solution  was  stirred  constantly 
during  the  heating  and  cooling.  The  viscosity  was  measured 
immediately  after  the  solution  was  cooled  to  24°C.  The  measure- 
ments were  all  made  at  24°C.  by  using  the  time  of  outflow 
through  a  viscometer.  The  time  of  outflow  of  distilled  water 
through  the  Ostwald  viscometer  used  was  exactly  1  minute  at 

1  LOEB,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  85,  1920-21. 


THE   VALENCY  RULE  AND  THE  HOFMEISTER  SERIES  83 

24°C.     Each  measurement  of  viscosity  was  repeated  with  the 
same  gelatin  solution  and  the  beginning  and  the  end  of  a  series 


FIG.  22. — Curves  representing  relative  viscosity  of  0.8  per  cent  solution  of 
originally  isoelectric  gelatin  brought  to  different  pH.  The  curves  for  relative 
viscosity  of  gelatin  chloride,  phosphate,  and  oxalate  are  practically  identical. 
Relative  viscosity  is  given  as  time  of  outflow  of  gelatin  solution  divided  by  time 
of  outflow  of  water  through  viscometer  at  24°C. 

consisted  in  the  measurement  of  viscosity  of  isoelectric  gelatin. 
These  latter  measurements  agreed  in  all  experiments  within  1 


84 


THEORY  OF  COLLOIDAL  BEHAVIOR 


second  varying  only  between  80  and  81  seconds,  thus  guarantee- 
ing the  reproducible  character  of  the  experiment. 


FIG.  23. — Curves  representing  relative  viscosity  of  gelatin  succinate,  tartrate, 
and  citrate.  The  curves  are  practically  identical  with  those  for  the  viscosity  of 
gelatin  chloride  and  phosphate. 

The  results  can  be  given  briefly.  Figure  22  gives  the  curves 
for  the  relative  viscosity  of  0.8  per  cent  solutions  of  gelatin  chloride, 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES   85 


sulphate,  oxalate,  and  phosphate.  The  abscissae  are  the  pH  of 
the  gelatin  solutions,  the  ordinates  the  ratio  of  the  time  of  outflow 
of  the  gelatin  solutions  divided  by  the  time  of  outflow  of  pure 


6 


1  2  3  4       47  5 

FIG.  24. — Curves  representing  relative  viscosity  of  gelatin  acetate,  mono-,  di-, 
and  trichloracetate.  Curves  identical  with  those  for  gelatin  chloride  and 
phosphate. 

water.  For  the  sake  of  brevity  this  quotient  will  be  called 
the  relative  viscosity  of  the  gelatin  solution.  The  curves  for  the 
four  acids  all  rise  steeply  from  the  isoelectric  point  with  increasing 


86  THEORY  OF  COLLOIDAL  BEHAVIOR 

hydrogen  ion  concentration  until  they  reach  a  maximum  at  pH 
about  3.0  or  slightly  above.  The  curves  then  drop  again.  The 
curves  for  the  three  salts,  gelatin  chloride,  oxalate,  and  phosphate 
are  practically  identical  while  the  curve  for  gelatin  sulphate  is 
considerably  lower. 

Figure  23  gives  the  curves  for  the  viscosity  of  gelatin  citrate, 
tartrate,  and  succinate.  The  three  curves  are  practically 
identical  and  also  identical  with  the  curves  for  gelatin  chloride 
and  gelatin  phosphate  in  Fig.  22. 

Figure  24  gives  the  curves  for  the  viscosity  of  0.8  per  cent  solu- 
tions of  originally  isoelectric  gelatin  to  which  acetic  and  mono-, 
di-,  and  trichloracetic  acids  have  been  added.  The  curves  are 
again  identical  with  those  for  gelatin  chloride,  phosphate,  etc. 

The  titration  curves  with  alkalies  have  shown  that  Ca  and  Ba 
combine  with  proteins  in  equivalent  proportions  and  we  should 
hence  expect  that  the  viscosity  curves  for  Ba  and  Ca  proteinates 
would  be  lower  than  those  for  Li,  Na,  K,  and  NH4  proteinates. 
This  was  found  to  be  correct. 

In  experiments  on  the  viscosity  of  casein  solutions  the  limited 
degree  of  solubility  of  the  salts  of  casein  has  to  be  considered.  In 
the  region  from  4.7  to  3.0  or  even  a  trifle  below  neither  casein 
chloride  nor  casein  phosphate  is  sufficiently  soluble  to  permit 
the  preparation  of  a  1  per  cent  solution,  and  in  this  region  the  in- 
fluence of  casein  on  the  viscosity  of  water  is,  therefore,  negligible. 
The  curve  representing  the  relative  viscosity  of  1  per  cent  casein 
chloride  and  phosphate  solutions  (as  compared  with  that  of  pure 
water)  rises  sharply  at  pH  3.0.  With  a  further  increase  of  the 
hydrogen  ion  concentration  the  curve  falls  steadily  as  it  did  in 
the  case  of  the  curve  for  gelatin.  This  indicates  that  the  maxi- 
mum for  the  influence  of  casein  chloride  on  viscosity  lies  at  pH 
equal  to  or  greater  than  3.0.  The  curve  for  the  influence  of 
casein  phosphate  on  viscosity  coincides  with  the  curve  for 
casein  chloride. 

The  difference  between  the  viscosity  curve  of  Na  caseinate 
and  Ba  caseinate  (Fig.  25)  is  also  similar  to  that  of  the 
corresponding  gelatin  salts. 

In  the  influence  of  monovalent  or  bivalent  ions  on  those  physi- 
cal properties  of  proteins  which  are  characteristic  for  colloidal  be- 
havior only  the  valency  and  the  sign  of  charge  of  the  ion  play  a  role, 


THE  VALENCY  RULE  AND  THE  HOFMEISTER  SERIES    87 


while  ions  of  the  same  sign  of  charge  and  valency  have  similar 
effects.  In  the  second  part  of  the  book  it  will  be  shown  that  this 
is  due  to  the  fact  that  the  colloidal  behavior  is  the  expression  of 
the  forces  set  up  by  the  Donnan  equilibrium  and  in  the  equation 


pH   6 


10 


11 


12 


FIG.  25. — Curves  representing  relative  viscosity  of  Na  and   Ba  caseinate  for 

different  pH. 

for  this  equilibrium  only  the  sign  of  charge  and  valency  appear. 
It  is  also  obvious  that  it  would  have  been  impossible  to  arrive  at 
this  valency  rule  without  the  proof  of  the  stoichiometrical 
character  of  the  combination  of  proteins  with  acids  or  bases, 
especially  the  proof  that  weak  dibasic  and  tribasic  acids  combine 
in  the  range  of  pH  concerned  in  molecular  proportions. 


CHAPTER    VI 

THE  ACTION  OF  NEUTRAL  SALTS  ON  THE  PHYSICAL 
PROPERTIES  OF  PROTEINS 

1.  THE  DIFFERENCE  IN  THE  EFFECT  OF  ACIDS,  ALKALIES, 
AND  SALTS  ON  PROTEINS 

The  most  striking  proof  for  the  alleged  existence  of  specific 
ion  effects  on  proteins  (aside  from  those  due  to  valency  of  the 
ion),  seemed  to  have  been  furnished  by  experiments  on  the 
influence  of  neutral  salts  on  the  osmotic  pressure,  swelling,  and  the 
viscosity  of  protein  solutions. 

It  has  been  noticed  by  a  number  of  authors  that  the  influence 
of  neutral  salts  on  the  physical  properties  of  proteins  differs  from 
that  of  acids  and  bases,  and  various  attempts  have  been  made  to 
find  an  accurate  expression  for  this  difference.  Some  hold  that 
neutral  salts  form  "adsorption  compounds"  with  " electrically 
neutral,"  i.e.,  non-ionized,  protein  molecules,  in  which  both  ions 
of  the  salt  were  believed  to  be  simultaneously  adsorbed  by  the 
"neutral"  protein  molecule.1  This  idea  is  no  longer  tenable  for 
salt  solutions  of  low  concentration  since  the  experiments  with 
powdered  gelatin  discussed  in  Chapter  II  have  shown  that  only 
one  (or  practically  only  one)  of  the  two  ions  of  a  neutral  salt  can 
combine  at  one  time  with  a  protein.  At  the  isoelectric  point, 
i.e.,  at  pH  4.7,  gelatin  can  combine  with  neither  ion  of  a  neutral 
salt;  at  a  pH  >  4.7  only  the  metal  ion  of  the  neutral  salt  can  com- 
bine with  the  gelatin,  forming  metal  gelatinate ;  at  a  pH  <  4.7  only 
the  anion  of  the  neutral  salt  is  capable  of  combining  with  the 
protein,  forming  gelatin-acid  salts. 

R.  S.  Lillie  has  made  the  statement  that  while  acids  and  alkalies 
increase,  salts  depress  the  osmotic  pressure  of  gelatin.2  This 
statement,  while  it  was  the  expression  of  facts  actually  observed 

1  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912. 

2  LILLIE,  R.  S.,  Am.  J.  Physiol.,vol.  20,  p.  127,  1907-08. 

88 


THE  ACTION  OF  NEUTRAL  SALTS  89 

by  Lillie,  is  not  entirely  correct  owing  to  the  fact  that  the  influence 
of  the  hydrogen  ion  concentration  of  the  gelatin  solution  was  not 
taken  into  consideration.  It  was  shown  in  the  preceding  chapter 
that  if  acid  is  added  to  a  gelatin-acid  solution  of  a  pH  of  3.0  or 
below,  the  effect  is  practically  the  same  as  when  we  add  a  neutral 
salt,  namely,  a  diminution  of  the  osmotic  pressure  of  the  solution; 
and  that  when  alkali,  e.g.,  KOH,  is  added  to  a  solution  of  a  metal 
gelatinate  of  pH  11.0  or  above,  the  effect  is  also  a  similar  depres- 
sion of  the  osmotic  pressure  to  that  caused  by  the  addition  of 
KC1.  A  depression  is  also  noticed  when  some  acid  is  added  to  a 
solution  of  metal  gelatinate  or  when  some  alkali  is  added  to 
gelatin-acid  salts ;  since  in  both  cases  the  gelatin  is  brought  nearer 
to  the  isoelectric  point. 

It  is  also  incorrect  to  speak  of  an  antagonism  between  the 
effects  of  acids  and  salts,  since  the  facts  mentioned  show  that 
there  is  also  an  antagonism  between  little  and  much  acid;  thus, 
if  the  pH  of  a  gelatin-acid  salt  is  3.0,  a  further  addition  of  the 
same  acid  depresses  the  osmotic  pressure  or  viscosity.  The 
question  then  arises,  What  is  the  correct  expression  of  the  facts 
in  the  case? 

The  answer  seems  to  be  as  follows:  Suppose  the  pH  is  below 
but  near  that  of  the  isoelectric  point  of  a  protein  and  HC1  be 
added.  In  this  case  the  more  acid  is  added  the  more  non- 
ionogenic  protein  is  transformed  into  salt.  This  salt  formation 
raises  the  osmotic  pressure,  swelling,  and  viscosity  of  the  protein. 
This  agrees  with  the  views  of  Laqueur  and  Sackur,  and  of  Pauli. 
At  the  same  time  the  anion  of  the  acid  has  an  opposite,  namely 
a  depressing  effect.  The  addition  of  acid  has,  therefore,  two 
opposite  effects  on  the  osmotic  pressure,  viscosity,  and  swelling 
of  protein,  namely,  first,  an  augmenting  effect  due  to  increasing 
protein-salt  formation  with  increasing  hydrogen  ion  concentration, 
and  second,  a  depressing  effect  due  to  the  anion,  in  our  example 
Cl.  At  first,  the  augmenting  effect  increases  more  rapidly  than 
the  depressing  effect.  When,  however,  the  pH  of  the  protein 
solution  approaches  the  value  3.0  the  augmenting  influence  due 
to  the  formation  of  new  gelatin  chloride  grows  less  rapidly  with 
a  further  decrease  in  pfi  than  does  the  depressing  effect  of  the 
anion,  and  hence,  when  the  amount  of  acid  added  increases 
still  further,  the  depressing  effect  of  the  Cl  ion  prevails  over  the 


90  THEORY  OF  COLLOIDAL  BEHAVIOR 

augmenting  effect  of  the  H  ion.  The  true  reason  for  this  will 
appear  in  Chap.  VIII. 

When  an  alkali,  e.g.,  NaOH,  is  added  to  a  protein,  e.g.,  gelatin, 
with  a  pH  slightly  above  4.7,  at  first  more  of  the  non-ionogenic 
protein  is  transformed  into  metal  proteinate,  e.g.,  Na  gelatinate; 
and  this  raises  the  osmotic  pressure,  viscosity,  and  swelling 
rapidly  by  causing  an  increase  in  the  concentration  of  ionized 
protein  for  a  reason  which  will  be  given  later.  The  cation  of  the 
alkali,  the  Na  ion,  has  a  depressing  effect  on  these  properties, 
and  this  depressing  effect  begins  to  be  visible  when  the  pH 
exceeds  a  certain  value.  After  this,  with  a  further  addition  of 
alkali,  the  depressing  action  of  the  cation  (e.g.,  of  Na)  increases 
more  rapidly  than  the  augmenting  action  of  the  OH  ion. 

The  addition  of  neutral  salts  of  a  concentration  below  N/16 
to  isoelectric  gelatin  has  no  effect  on  osmotic  pressure,  viscosity, 
or  swelling  of  the  gelatin  solution.  When  neutral  salt  is  added 
to  a  gelatin  solution  on  either  side  of  its  isoelectric  point  only  a 
depressing  action  of  that  ion  which  has  the  opposite  sign  of 
charge  to  the  protein  ion  is  observed.  No  augmenting  action  of 
the  ion  with  the  same  sign  of  charge  as  the  protein  is  noticeable. 
Thus,  if  CaC^or  Na2SO4  is  added  to  a  solution  of  gelatin  chloride 
or  gelatin  nitrate  only  a  depressing  effect  of  the  Cl  or  SO4  ion 
is  observed  but  no  augmenting  effect  of  the  Ca  or  Na  ion;  while 
when  these  salts  are  added  to  a  solution  of  a  metal  gelatinate  only 
a  depressing  effect  of  the  Ca  or  Na  ion  is  apparent  but  no  aug- 
menting effect  of  the  anion.1  The  theoretical  reason  for  these 
effects  will  be  given  in  Chap.  VIII. 

An  approximately  1.6  per  cent  solution  of  isoelectric  gelatin 
was  prepared  and  brought  to  a  pH  of  4.0.  The  solution  was  made 
0.8  per  cent  in  regard  to  the  originally  isoelectric  gelatin  by  adding 
to  50  c.c.  of  the  1.6  per  cent  solution  either  50  c.c.  of  H2O  or  of  a 
salt  solution,  e.g.,  NaCl,  of  different  molecular  concentration, 
from  M/8,192  to  1  M,  taking  care  that  the  hydrogen  ion  concen- 
tration remained  the  same.  The  time  of  outflow  through  a 
viscometer  was  determined  in  the  way  described  in  Chap.  V, 
and  the  ratios  of  the  time  of  outflow  to  that  of  water  were  plotted 
as  ordinates  over  the  pH  as  abscissae  (lower  curve,  Fig.  26).  We 

1  The  contents  of  this  chapter  are  based  on  LOEB,  J.,  J.  Gen.  Physiol., 
vol.  3,  p.  391,  1920-21. 


THE  ACTION  OF  NEUTRAL  SALTS 


91 


will  designate  this  value  as  relative  viscosity.     The  addition 
of  the  NaCl  causes  only  a  drop,  and  no  rise  in  the  curve. 


LO 

nMlLN-KKKKN   N   N   N 
U  8192409620481024512  256  128  64  32    16     8 

Concentration 

FIG.  26.— Difference  in  the  effect  of  different  concentrations  of  NaCl  and  of 
HC1  on  the  relative  viscosity  of  an  0.8  per  cent  solution  of  gelatin  chloride  of 
pH  4.0.  In  the  case  of  NaCl  we  observe  only  the  depressing  effect  of  the  Cl  ion; 
in  the  case  of  HC1  we  notice  an  augmenting  effect  of  the  H  ion  and  a  depressing 
effect  of  the  Cl  ion,  the  latter  prevailing  as  soon  as  the  concentration  of  acid 
added  is  >  N/256. 

If,  however,  the  1.6  per  cent  gelatin  solution  of  pH  4.0  is  mixed 
with  various  concentrations  of  HC1  (upper  curve,  Fig.  26)  instead 


92 


THEORY  OF  COLLOIDAL  BEHAVIOR 


of  with  NaCl,  at  first  a  rise  occurs  which  is  followed  by  a  drop 
when  the  concentration  of  the  Cl  ion  is  a  little  above  N/ 1,000. 
In  Fig.  26  the  drop  appears  at  a  concentration  of  about  N/256  HC1, 
but  the  reader  must  remember  that  on  account  of  the  fact  that 


\ 


\ 


'\ 


Xk 


28 
2.7 
26 
25 
24 
23 
2.2 

Z1 
20 

1.9 

"> 

1-7 

1.6 

15 
1.4 
1.3 
12 
1.1 


Concentotion 

FIG.  27. — The  relative  viscosity  of  0.8  per  cent  solution  of  gelatin  chloride 
of  pH  3.0  is  depressed  almost  equally  by  the  Cl  ion  of  HC1  as  of  NaCl.  The 
augmenting  effect  of  the  H  ion  in  the  case  of  HC1  is  no  longer  noticeable. 

part  of  the  acid  combined  with  the  gelatin  the  pH  of  the  solution 
was  about  3.0.  In  other  words,  while  the  addition  of  H  ions 
increases  the  viscosity  of  a  solution  of  gelatin  chloride  of  pH  4.0, 
the  addition  of  Na  ions  does  not  have  such  an  effect,  but  the  Cl 
ion  depresses  the  viscosity  in  both  cases,  no  matter  whether 
NaCl  or  HC1  is  added  to  the  gelatin  solution;  and  the  depressing 
action  of  the  Cl  ion  increases  with  its  concentration.  Moreover, 


THE  ACTION  OF  NEUTRAL  SALTS 


93 


the  increase  of  the  viscosity  by  the  H  ions  stops  as  soon  as  the 
pH  of  the  solution  reaches  about  3.0  for  the  reason  stated. 

When  the  same  experiment  is  repeated  with  a  gelatin  solution 
of  pH  3.0,  the  addition  of  NaCl  immediately  causes  a  drop  also 


8 


I 


£4 
2.3 
2.2 
2.1 
20 
1.9 
1.8 
1.7 
1.6 
1.5 
1.4 

1.2 
1.1 
1.0 


Concentration 

FIG.  28.— When  the  gelatin  solution  has  a  pH  of  2.5,  HC1  and  NaCl  depress  the 
relative  viscosity  of  the  gelatin  solution  to  the  same  degree. 

(Fig.  27)  while  the  addition  of  HC1  no  longer  causes  a  rise  but 
the  drop  commences  a  little  later  than  in  the  case  of  NaCl. 

When,  however,  the  same  experiment  is  made  with  a  gelatin 
solution  of  pH  2.5  (Fig.  28),  an  immediate  drop  is  noticed  upon 
the  addition  of  HC1  as  well  as  in  the  case  of  the  addition  of  NaCl, 


M 


94 


THEORY  OF  COLLOIDAL  BEHAVIOR 


and  the  curve  for  HC1  coincides  practically  with  that  for  NaCl, 
as  our  theory  demands. 

That  the  depression  of  the  viscosity  of  gelatin  chloride  due  to 
the  presence  of  a  salt  is  exclusively  determined  by  the  anion  of 


Concentration 

FIG.  29. — The  depressing  effect  of  equal  molecular  concentrations  of  NaCl, 
CaCh,  and  LaCU  on  the  relative  viscosity  of  0.8  per  cent  gelatin  chloride  solution 
of  pH  3.0  is  roughly  in  proportion  to  the  concentration  of  the  Cl  ions  in  the 
solutions;  i.e.,  as  1:2:3. 

the  salt  and  that  the  cation  has  no  augmenting  effect  is  shown 
in  Fig.  29,  where  the  influence  of  NaCl,  CaCl2,  and  LaCl3  upon 
the  viscosity  of  gelatin  of  pH  3.0  is  represented.  Fifty  cubic  centi- 
meters of  a  1.6  per  cent  solution  of  gelatin  chloride  of  pH  3.0  were 
added  to  50  c.c.  of  a  solution  of  different  concentrations  of  each 
salt  as  described,  the  pH  being  kept  at  3.0.  It  is  obvious  from 


THE  ACTION  OF  NEUTRAL  SALTS 


95 


Fig.  29  that  the  molecular  concentrations  of  NaCl,  CaCU,  and 
LaCl3,  which  depress  the  viscosity  to  the  same  level  are  approxi- 
mately in  the  ratio  of  3:2:1.  Thus,  when  the  effect  of  NaCl  and 


2.8 
2.7 
£6 
25 

2.4 
2.3 
£2 
2.1 
20 
1.9 
1.8 
1.7 
1.6 
1.5 
L4 
1.3 
1.2 
1.1 
1.0 


:\ 


\ 


Nv 


^r4 


0    SI92  4096 


512  256  128  64    32    16     8 


|  IN 


Concentration  of  Cl 


FIG.  30. — Showing  that  NaCl  and  CaCh  have  the  same  depressing'effect  on  the 
viscosity  of  gelatin  chloride  of  pH  =  3.0  when  the  concentration  of  Cl  ions  is 
the  same. 

CaCl2  is  plotted  over  the  same  concentration  of  the  Cl  ions  the 
curves  for  the  salts  become  nearly  identical  (Fig.  30),  and  the  same 
would  be  practically  true  for  the  LaCl3  curve.  From  this  it  follows 


96 


THEORY  OF  COLLOIDAL  BEHAVIOR 


that  the  depressing  effect  of  these  three  salts  on  gelatin  chloride 
is  practically  exclusively  a  function  of  the  concentration  of  the 


4096  2048 1021  512  256  128  64    32    1 

Concentration 

FIG.  31. — The  relative  depressing  effect  of  equal  molecular  concentrations 
of  NaCl,  Na2SO4,  and  Na4Fe(CN)e  on  the  relative  viscosity  of  a  gelatin  chloride 
solution  of  pH  3.0  is  approximately  as  1:4: 16. 


Cl  ion,  while  no  augmenting  effect  of  the  cation  is  noticeable. 
This  observation  disposes  of  vague  hints  found  in  the  literature 


THE  ACTION  OF  NEUTRAL  SALTS  97 

of  colloids  that  the  opposite  ions  of  a  neutral  salt  affect  the  prop- 
erties of  a  protein  in  an  opposite  direction.  We  made  sure 
that  in  all  these  cases  the  pH  of  the  gelatin  solution  was  not 
altered  by  the  addition  of  the  salt. 

When  0.8  per  cent  solutions  of  gelatin  chloride  of  pH  3.0  are 
prepared  in  solutions  of  Na  salts  with  the  anion  of  a  weaker 
acid,  e.g.,  Na2  oxalate,  Na4Fe(CN)6,  the  pH  is  increased  and 
there  exists  the  danger  of  erroneously  attributing  a  depressing 
effect  to  the  anion  which  in  reality  is  caused  by  the  increase  in 
pH.  In  Fig.  31  the  effects  of  the  addition  of  equal  concentrations 
of  Nad,  Na2SO4,  and  Na4Fe(CN)6  on  gelatin  chloride  of  pH  = 
3.0  are  plotted.  In  the  case  of  Na4Fe(CN)6  only  the  lowest 
concentrations,  from  M/8,192  to  M/ 1,024,  could  be  used,  since 
in  these  only  did  the  pH  of  the  protein  solution  remain  =  3.0. 
Figure  31  shows  that  the  depressing  effect  of  these  salts  increases 
rapidly  with  the  valency  of  the  anion.  When  the  concentration 
of  the  salt  was  only  M/ 1,024  a  drop  in  the  viscosity  was  already 
noticeable.  This  drop  was  small  in  the  case  of  NaCl  (from  2.8 
to  2.6),  was  greater  in  the  case  of  Na2S04  (from  2.8  to  2.35), 
and  considerably  greater  in  the  case  of  Na4Fe(CN)6  (from  2.8 
to  1.5).  The  objection  might  be  raised  that  since  Na2SO4  has 
twice  as  many  cations  as  NaCl  of  the  same  concentration  and 
Na4Fe(CN)6  has  four  times  as  many  cations,  it  was  the  difference 
in  the  concentration  of  the  cations  which  caused  the  difference 
in  the  drop.  This  is  refuted  by  the  fact  that  Na2SO4  causes  a 
drop  in  the  specific  viscosity  to  1.8  at  a  concentration  of  M/256 
while  NaCl  causes  the  same  drop  at  a  concentration  of  above 
M/64  which  is  about  four  times  as  high.  If  the  concentration 
of  the  cation  were  responsible  for  the  drop  the  two  concentrations 
should  be  more  nearly  as  1 : 2.  Na4Fe(CN)  6  causes  the  same  drop 
of  the  viscosity  to  1.8  at  a  concentration  less  than  M/  1,024. 
Hence,  the  concentration  of  Na4Fe(CN)6  required  to  cause  the 
same  diminution  of  the  specific  viscosity  as  that  caused  by  M/64 
NaCl  is  less  than  one-sixteenth  of  the  latter,  while  it  should  be 
only  one-fourth  if  the  cation  were  responsible  for  the  drop. 

Experiments  on  osmotic  pressure  and  on  swelling  lead  to  the 
same  formulation  of  the  difference  in  the  effect  of  acids  and  salts 
as  the  viscosity  experiments. 

What  has  been  shown  for  the  effect  of  acids  on  the  physical 

7 


98 


THEORY  OF  COLLOIDAL  BEHAVIOR 


properties  of  proteins  can  also  be  shown  for  the  influence  of 
alkalies.  Thus,  the  addition  of  KOH  to  Na  gelatinate  of  pH  12.0 
depresses  the  viscosity  in  the  same  way  as  the  addition  of  KC1 
(Fig.  32) ;  while  the  addition  of  little  KOH  to  Na  gelatinate  of 
pH  4.8  to  8.0  increases  the  viscosity,  and  the  addition  of  KC1  to 
Na  gelatinate  always  depresses  the  viscosity.  The  depressing 
effect  of  salts  on  the  viscosity  of  solutions  of  metal  gelatinate  is 


1 


2.0 
1.9 

1.8 
1.7 
1.6 
1.5 
1.4 
1.3 
1.2 
1.1 
1  n 

KOI 

?[•. 

ft5 

~^1  f. 

I    I 

S* 

c 

^ 

k 

c 

\, 
c 

N^ 

i( 
< 

>v/ 

1 

ft.JdL  1L  JtLliJl  JHL 11  M  ^^ 

u  6192409620451024512  256  1Z8   64    32   16 

Concentration 

FIG.  32. — The  depressing  effect  of  KOH  and  KC1  on  Na  gelatinate  of  pH  12.0 
is  practically  the  same. 

due  to  the  cation  of  the  salt  added,  that  of  bivalent  cations 
being  greater  than  that  of  monovalent  cations,  while  the  valency 
of  the  anion  has  no  effect. 

We  have  already  stated  that  the  addition  of  neutral  salt  to 
isoelectric  gelatin  leaves  the  viscosity  and  osmotic  pressure  of  the 
solution  practically  unchanged.  This  fact  is  of  great  importance 
for  the  theory  of  colloids. 

The  depressing  effect  of  neutral  salts  on  the  physical  prop- 
erties of  proteins  is,  therefore,  the  same  phenomenon  as  the 
drop  in  the  curves  of  these  properties  when  too  much  acid  or  too 
much  alkali  has  been  added.  It  is  due  to  the  fact  that  in  all 


THE  ACTION  OF  NEUTRAL  SALTS  99 

cases  that  ion  which  has  the  opposite  sign  of  charge  to  that  of 
the  protein  ion  depresses  the  osmotic  pressure,  swelling,  and 
viscosity  of  proteins. 

2.  ION  SERIES  AND  THE  ACTION  OF  SALTS  ON  PROTEINS 

From  what  has  been  said,  it  is  clear  that  only  one  of  the  ions  of 
a  neutral  salt  influences  the  physical  properties  of  a  protein, 
namely  that  ion  which  has  the  opposite  sign  of  charge  to  the 
protein  ion;  and  this  influence  is  of  a  depressing  character.  We 
will  now  show  that  this  effect  depends  only  upon  the  valency  of 
the  depressing  ion  and  that  different  ions  of  the  same  valency 
have  the  same  depressing  effect.  It  is  necessary  to  compare  the 
relative  depressing  action  of  low  but  equal  concentrations  of 
different  salts  upon  the  physical  properties  of  a  gelatin  salt,  for 
example,  gelatin  chloride  of  a  definite  pH;  e.g.,  3.0.  As  can  be 
easily  surmised,  the  addition  of  a  salt  will  in  many  cases  alter  the 
pH  of  the  solution  and  this  alteration  will  be  larger  in  the  case  of 
certain  salts,  e.g.,  Na  acetate,  than  in  the  case  of  others,  e.g., 
NaCl.  Unless  we  take  into  consideration  these  variations  in  the 
pH  caused  by  the  addition  of  salts  there  will  be  danger  of 
erroneously  ascribing  the  influence  of  a  variation  in  the  hydrogen 
ion  concentration  to  an  influence  of  the  nature  of  the  anion. 
The  Hofmeister  ion  series,  as  far  as  they  refer  to  proteins,  are 
largely  due  to  this  error. 

The  method  of  our  experiments  was  as  follows:  50  c.c.  of  a  1.6 
per  cent  solution  of  originally  isoelectric  gelatin  contained  enough 
HC1  to  make  the  pH  =  3.0.  To  this  were  added  50  c.c.  of  H2O 
or  of  a  salt  solution  of  different  molecular  concentration,  and  the 
viscosity  of  this  mixture  was  measured  using  those  precautions 
which  were  described  in  the  preceding  chapter. 

Figure  33  gives  the  curves  representing  the  depression  of  the 
relative  viscosity  of  a  gelatin  chloride  solution  of  pH  3.0  by  dif- 
ferent concentrations  of  salts  with  monovalent  anion;  namely, 
NaCl,  NaH2PO4,  NaCNS,  NaH  tartrate,  NaH2  citrate,  and  Na 
acetate.  The  curve  for  Na2SO4  is  added  for  comparison.  The 
monosodium  salts  of  weak  dibasic  and  tribasic  acids  dissociate 
electrolytically  into  a  Na  ion  and  a  monovalent  anion,  H2PO4,  H 
tartrate,  H2  citrate,  etc.  All  the  salts  mentioned  in  Fig.  33  are 
therefore  salts  with  monovalent  anion  with  the  exception  of 


100  THEORY  OF  COLLOIDAL  BEHAVIOR 

.     Our  valency  rule  demands  that  the  relative  depressing 


M 


ft  ft  ft  fe  f  9 : 9 


Concentration. 

FIG.  33. — The  depressing  effect  of  different  salts  with  monovalent  anion 
(NaCl,  NaH2PO4,  NaCNS,  NaH  tartrate,  and  NaH2  citrate)  on  the  relative 
viscosity  of  0.8  per  cent  solution  of  gelatin  chloride  of  pH  3.0.  The  effects  of 
NaCl  and  NaHzPCh  are  identical  since  the  pH  is  not  altered  by  the  addition  of 
these  salts.  The  depression  in  the  values  for  the  relative  viscosity  is  greater  in 
the  case  of  Na  acetate  than  in  the  case  of  NaCl  for  the  reason  that  the  Na  acetate 
raises  the  pH  of  the  gelatin  chloride  solution. 


effect  of  these  salts  (with  the  exception  of  Na2SO4)  should  be 


THE  ACTION  OF  NEUTRAL  SALTS 


101 


nearly  the  same  and  that  deviations  from  this  rule  should  find 
their  explanation  in  corresponding  deviations  of  the  pH  due  to  the 
influence  of  certain  of  the  salts.  We  will  first  consider  this  latter 
influence  as  given  in  Table  VI,  which  shows  the  results  of  the 

TABLE  VI. — CHANGES  IN  pH  OF  0.8  PEE  CENT  GELATIN  CHLORIDE  OF 
pH  =  3.0  UPON  ADDITION  OF  VARIOUS  CONCENTRATIONS  OF  SALTS 


Molecular  concentrations  of  salts  used 

0 

i-H 

ocf 

3 

1 

00 

1 

^ 

i—  r 

— 

§ 

•s* 

| 

CO 

^ 

s 
1st 

oo 
^ 

1 

NaCl...  

3  0 

3.0 
3.0 
3.0 
3.0 
3.0 
3.0 
3.0 

3.0 
3.0 
3.0 
3.0 
3.0 
3.0 
3.0 

3.0 
3.0 
3.0 
3.0 
3.0 
3.0 
3.05 

3.0 
3.0 
3.0 
3.0 
3.0 
3.0 
3.1 

3.0 
3.0 
3.0 
3.0 
3.0 
3.1 
3.3 

3.0 
3.0 
3.0 
3.1 
3.1 
3.2 
3.7 

3.0 
3.0 
3.1 
3.2 
3.3 
3.4 
4.3 

3.0 
3.05 
3.2 
3.3 
3.45 
3.6 
4.6 

3.0 
3.1 
3.3 
3.6 
3.5 
3.7 

3.0 
3.2 
3.4 
3.9 
3.55 
3.75 

3.0 
3.3 

3.45 
4.2 

3.0 
3.35 
3.5 
4.4 

Na2SO4  

3.0 
3.0 
3.0 
3.0 
3.0 
3.0 

NaH2PO4  
NaCNS  

NaH  tartrate  
NaH2  citrate  
Na  acetate  

measurements  of  pH  in  these  different  gelatin  solutions  after 
the  addition  of  salts.  The  original  gelatin  chloride  solution  had 
a  pH  of  about  3.0  and  the  pH  was  not  altered  by  the  addition  of 
NaCl  and  only  slightly  by  the  addition  of  NaH2PO4  in  con- 
centrations below  M/16.  According  to  the  valency  rule  the 
curves  for  the  depressing  effect  of  NaCl  and  NaH2P04  should  be 
almost  identical  and  Fig.  33  shows  that  this  is  the  case. 

Table  VI  shows  that  NaCNS,  monosodium  tartrate,  and  mono- 
sodium  citrate  raise  the  pH  of  the  solution  as  soon  as  the  con- 
centration reaches  M/128  or  more.  If  we  consider  this  effect, 
we  must  expect  to  find  that  the  drop  in  the  curves  for  NaCNS, 
monosodium  citrate,  and  monosodium  tartrate  is  a  little  steeper 
in  concentrations  of  M/128  and  above  than  the  curve  for  the 
depressing  effect  of  NaCl.  Figure  33  shows  that  the  curves  for 
the  depressing  effect  of  these  three  salts  are  slightly  lower  than 
the  curve  for  NaCl  or  NaH2PO4.  The  greatest  apparent 
deviation  from  the  valency  rule  occurs  in  the  curve  for  Na  acetate 
whose  depressing  effect  is  of  the  order  of  that  of  Na2SO4. 

In  the  colloidal  literature  it  is  always  stated  that  Na  acetate 
acts  like  Na2SO4  and  this  is  interpreted  to  mean  that  the  acetate 


102 


THEORY  OF  COLLOIDAL  BEHAVIOR 


anion  acts  like  the  bivalent  SO4  anion  and  not  like  the  monovalent 
Cl  or  NO3  anion.  Table  VI  shows  that  Na  acetate  also  depresses 
the  hydrogen  ion  concentration  more  than  NaCl  or  NaH2PO4; 


2.8 
2.7 
2.6 
2.5 
2.4 
2.3 
&   22 

8     2.1 
to 
>     2.0 

1     L9 
33     1-8 
&     1.7 
1.6 
1.5 
1.4 
L3 
1.2 
1.1 
i  r» 

t  — 

— 

^i 

5 

k^ 

\ 

ft 

< 

^      V^ 

\ 

1 

,^ 

a 

\ 

\ 

\  *§> 
\ 

Aj 

> 

i 

\  j 

\ 

\ 

N 

» 

PH 

=  3.. 

j 

M     M    M 


M    M.  H   M    M    M    M 
512  256  128  64   32    16 


Concentration 

FIG.  34. — When  the  pH  is  kept  equal  the  depressing  effect  of  equal  concentra- 
tions of  NaCl  and  Na  acetate  on  the  relative  viscosity  of  an  0.8  per  cent  gelatin 
chloride  or  gelatin  acetate  solution  of  pH  3.3  is  the  same. 

M/64  Na  acetate  brings  the  gelatin  solution  practically  to  the 
isoelectric  point,  and  at  the  isoelectric  point  the  viscosity  of 
gelatin  solution  is  a  minimum.  This  lowering  of  the  hydrogen  ion 


THE  ACTION  OF  NEUTRAL  SALTS  103 

concentration  (and  not  the  alleged  influence  of  the  acetate  anion) 
explains  the  excessive  depressing  effect  of  Na  acetate.  That 
this  interpretation  is  correct  can  be  proved  in  the  following  way: 
0.8  per  cent  solutions  of  gelatin  acetate  of  pH  3.3  and  gelatin 
chloride  also  of  pH  3.3  were  prepared.  The  relative  viscosity 
of  these  two  solutions  was  practically  the  same  (both  were  0.8 
per  cent  solutions  in  regard  to  originally  isoelectric  gelatin). 
The  solution  of  gelatin  acetate  of  pH  3.3  was  made  up  in  various 
concentrations  of  Na  acetate  of  pH  3.3.  The  Na  acetate  solu- 
tion of  pH  3.3  was  obtained  by  dissolving  M/16  Na  acetate  in 
IJ^J  M  acetic  acid  and  the  various  degrees  of  dilution  of  this 
M/16  Na  acetate  solution  of  pH  3.3  were  brought  about  by 
dilution  with  pure  acetic  acid  of  pH  3.3.  The  non-dissociated 
molecules  of  acetic  acid  have  no  more  depressing  influence  on 
the  physical  properties  of  proteins  than  have  the  molecules  of 
any  non-electrolyte.  Figure  34  gives  the  curve  representing  the 
depressing  effect  of  Na  acetate  on  gelatin  acetate  of  pH  3.3,  when 
the  pH  is  kept  constant. 

The  gelatin  chloride  solution  of  pH  3.3  was  made  up  in  different 
concentrations  of  NaCl  and  the  depressing  effect  of  NaCl  on  the 
viscosity  of  gelatin  chloride  is  also  plotted  in  Fig.  34.  It  is 
obvious  from  Fig.  34  that  the  depressing  effects  of  Na  acetate 
and  NaCl  are  identical  when  the  pH  is  kept  constant  and  identical 
in  both  cases. 

The  same  fact  was  confirmed  in  a  somewhat  different  way. 
A  1.6  per  cent  solution  of  gelatin  chloride  of  pH  3.0  was  made  up 
in  various  concentrations  of  Na  acetate  also  of  pH  3.0.  In 
order  to  prepare  Na  acetate  solutions  of  pH  3.0,  M/4  Na  acetate 
was  dissolved  in  M/4  HC1  and  the  various  dilutions  required  for 
the  experiment  were  obtained  by  diluting  the  mixture  of  equal 
parts  of  M/4  HC1  and  M/4  Na  acetate  with  M/1,000  HC1. 

The  1.6  per  cent  gelatin  chloride  solution  of  pH  3.0  was  diluted 
with  50  c.c.  of  this  mixture  so  that  the  resulting  0.8  per  cent 
gelatin  chloride  solution  of  pH  3.0  contained  various  concentra- 
tions of  Na  acetate  (or  more  correctly  of  NaCl  and  Na  acetate). 
The  curve  representing  the  depressing  effect  of  this  salt  is  given 
in  Fig.  35,  and  is  shown  to  be  identical  with  the  curve  representing 
the  depressing  effect  of  the  addition  of  NaCl  to  gelatin  chloride 
of  pH  3.0. 


104 


THEORY  OF  COLLOIDAL  BEHAVIOR 


We  can,  therefore,  state  that  sodium  acetate  has  the  same  effect 
on  the  viscosity  of  gelatin  chloride  as  the  addition  of  any  other 
salt  with  monovalent  anion,  and  that  the  anomalous  effect 


2.8 
2.7 
2.6 
2.5 
2.4 
2.3 

f  » 

£  21 

>     2.0 
1     « 

1    » 

^     1.7 
1.6 
1.5 
1.4 
1.3 
1.2 

1.1 
1  n 

] 

h—  — 

^ 

> 

v._ 

^ 

\ 

i( 

c 

K, 

i 

\ 

< 

^ 

J 

\ 

ic^ 

X 

\ 

1     ^^ 

c 

V 

9^, 

\ 

^ 

i 

^ 

\ 

X 

1 

\ 

1 

r  N 

I 

X, 

pH 

=  3.C 

ft     M    M    M    M    M    M    M    M    M    M 

U   8192409620481024512  256  128    64    32    16 

Concentration 

Fio.  35. — vSee  legend  of  Fig.  34,  except  that  the  pH  of  gelatin  solution  is  3.0. 

ascribed  to  the  acetate  anion  in  the  colloidal  literature  is  in 
reality  due  to  the  depression  of  the  hydrogen  ion  concentration 
of  the  gelatin  solution  by  the  Na  acetate,  which  is  a  buffer  salt, 


THE  ACTION  OF  NEUTRAL  SALTS 


105 


The  failure  to  recognize  the  buffer  character  of  salts,  like  the 
acetates,  citrates,  and  tartrates,  has  led  to  the  error  of  the  Hof- 
meister  ion  series.  In  reality  we  find  our  valency  rule  confirmed 
whereby  all  salts  with  an  anion  of  the  same  valency  have  about 
the  same  relative  depressing  effect  on  the  viscosity  of  a  gelatin 
chloride  solution  if  the  pH  of  the  solution  is  kept  constant. 


B    ^ 

<&      55 
CP    50 
32     45 
2_    40 

d     35 
J?    30 

^"    25 

§ 

S      20 

.ZJ 

1      15 
*>      10 
S       5 
f£       0 

i 

"1 

^ 

tl 

x 

N 

2 

r 

• 
K 

\ 

V 

px  \ 

\ 

k  <^ 

/». 

•^ 

*^*  < 

M 

B 

M 

p 

j-> 

A 

1 

• 

•\ 

a 

*   5 

;    j 

\ 

i 

k 

i 

\ 
4 

k 

A 

N 

| 

^ 

k 

NBP 

4 

3 

^s 

^ 

: 

°Na 

ma 

^n\ 

fp, 

N 

k 

— 

*Na 

Hpd 

trat 

i 

0   8192  4096  Z048  1024  512  256  128   64    32   16    ^ 

Concentration 

FIG.  36. — Showing  that  the  depressing  effect  of  salts  with  monovalent  anion 
on  the  swelling  of  gelatin  chloride  of  pH  3.3  is  similar  to  that  on  the  relative 
viscosity.  All  salts  with  monovalent  anion  depress  the  swelling  of  gelatin  chlor- 
ide to  the  same  extent,  the  seeming  deviation  from  this  rule  being  due  to  variation 
in  the  pH  of  the  gelatin  solution  caused  by  buffer  salts. 

What  has  been  demonstrated  for  the  effect  of  these  salts  on  the 
viscosity  of  gelatin  solutions  holds  also  for  their  effect  on  the 
swelling  of  gelatin.  The  same  volumetric  method  for  measuring 
the  swelling  effect  was  used  which  was  described  in  the  preceding 
chapter.  Figure  36  gives  the  relative  depressing  effect  of  NaCl, 
NaH2P04,  NaCNS,  monosodium  tartrate,  monosodium  citrate, 


106 


THEORY  OF  COLLOIDAL  BEHAVIOR 


and  Na  acetate  on  the  swelling  of  gelatin  chloride  of  pH  3.3 
(the  curve  for  Na2S04  is  added  for  comparison),  and  Table  VII 
gives  the  variation  of  the  pH  of  the  gelatin  caused  by  the  addition 
of  these  salts.  Our  theory  demands  that  all  these  salts  (except 
Na2SO4)  should  depress  the  swelling  of  gelatin  chloride  of  pH 
3.3  to  the  same  amount,  and  that  deviations  from  this  rule 

TABLE  VII. — CHANGES  IN  pH  OF  0.8  PER  CENT  GELATIN  CHLORIDE  OF 
pH  =  3.3  UPON  ADDITION  OF  VARIOUS  CONCENTRATIONS  OF  SALTS 


Molecular  concentrations  of  salts  used 

o 

O5 
l-H 

GO" 

1 

M/2,048 

1 
i—  1 

a 

i—  i 

1 

§ 

CO 

5 

CO 

CO 

GO 

NaCl     

3.3 
3.3 
3.3 
3.3 
3.3 
3.3 
3.3 

3.3 
3.3 
3.3 
3.3 
3.3 
3.3 
3.3 

3.3 
3.3 
3.3 
3.3 
3.3 
3.3 
3.3 

3.3 
3.3 
3.3 
3.3 
3.3 
3.3 
3.4 

3.3 
3.3 
3.3 
3.3 
3.3 
3.3 
3.45 

3.3 
3.3 
3.3 
3.3 
3.4 
3.4 
3.5 

3.3 
3.3 
3.3 
3.3 
3.5 
3.5 
3.8 

3.3 
3.3 
3.3 
3.3 
3.5 
3.6 
4.3 

3.3 
3.35 
3.4 
3.3 
3.6 
3.8 
4.8 

3.3 
3.4 
3.5 
%3.3 
3.7 
3.85 
5.2 

3.3 
3.5 
3.6 
3.35 
3.7 
3.9 
5.4 

3.3 
3.6 
3.7 
3.4 
3.7 
3.9 
5.5 

Na2SO4 

NaH2PO4  

NaCNS 

NaH  tartrate  
NaH2  citrate  
Na  acetate 

must  find  their  explanation  in  variations  of  pH  caused  by  the 
addition  of  salt.  Table  VII  shows  that  the  variations  in  pH  are 
small  for  NaCl,  NaCNS,  and  NaH2PO4  and  hence,  the  curves 
for  the  depressing  effect  of  these  three  salts  upon  the  swelling  of 
gelatin  are  almost  identical,  as  the  valency  rule  demands.  Mono- 
sodium  citrate  and  tartrate  have  a  greater  depressing  effect  on 
the  hydrogen  ion  concentration  and  Na  acetate  has  a  still  greater 
depressing  effect  than  these  two  salts.  This  explains  the  appar- 
ent deviation  of  the  curves  for  these  three  salts  from  the  valency 
rule. 

A.  D.  Hirschfelder1  has  published  a  paper  on  the  effects  of 
different  salts  on  the  swelling  of  fibrin  in  HC1  in  which  he  showed 
that  the  effect  of  citrates,  acetates,  and  phosphates  on  swelling 
was  the  same  as  that  of  chlorides,  bromides,  and  nitrates  if  the 
hydrogen  ion  concentration  was  kept  constant;  only  the  sulphates 
had  a  greater  depressing  effect.  The  influence  of  salts  on  the 

1  Hirschfelder,  A.  D.,  J.  Am.  Med.  Ass.,  vol.  67,  p.  1891,  1916. 


THE  ACTION  OF  NEUTRAL  SALTS 


107 


swelling  of  fibrin  is,  therefore,  identical  with  the  influence  of 
salts  on  the  swelling  of  gelatin. 

The  osmotic  pressure,  viscosity,  and  swelling  of  Na  gelatinate 
should  be  depressed  by  the  cation  of  a  salt  and  the  more  so  the 
higher  the  valency  of  the  cation.  Figure  37  shows  that  this  is 
true  for  the  swelling  of  Na  gelatinate  of  pH  about  9.3.  The 
molecular  concentration  in  which  the  swelling  is  depressed  by  the 


'2048 1C 

Concentration 

FIG.  37. — The  depressing  effect  of  neutral  salts  on  the  swelling  of  Na  gelatinate 
of  pH  about  9.3  is  due  to  the  cation  of  the  salt,  the  depressing  effect  of  NaCl  being 
half  as  great  as  that  of  NasSC^  of  equal  molecular  concentration  of  Na2SO4  while 
that  of  CaCh  is  considerably  greater  owing  to  the  fact  that  Ca  is  bivalent. 

same  amount  is  about  half  as  great  for  Na2S04  as  for  NaCl 
(for  molecular  concentrations  from  M/256  to  M/32),  while  it  is 
about  eight  times  as  high  for  NaCl  as  for  CaCl2,  roughly  proving 
that  the  cation  is  responsible  for  the  depression.  The  pH  of 
the  gelatin  was  practically  the  same  in  all  solutions. 

All  these  data  confirm  our  valency  rule,  whereby  ions  of  the 
same  valency  and  the  same  sign  of  charge  have,  in  the  same 
concentration,  nearly  the  same  depressing  effect  on  osmotic 
pressure,  swelling,  and  viscosity  of  proteins;  while  the  depressing 
effect  increases  rapidly  with  the  valency.  The  Hofmeister  ion 


108  THEORY  OF  COLLOIDAL  BEHAVIOR 

series  are  chiefly  due  to  the  failure  to  measure  the  influence 
of  the  salts  on  the  hydrogen  ion  concentration  of  the  gelatin 
solutions.  This  neglect  has  given  rise  to  the  statement  that 
salts  like  sodium  acetate  have  the  same  depressing  effect  on 
the  physical  properties  of  proteins  as  the  sulphates. 

Neutral  salts,  when  added  in  low  concentrations — i.e.,  below 
M/16 — affect  the  physical  properties  of  proteins  in  two  different 
ways:  first,  by  an  exchange  of  one  of  the  ions  of  the  salt  for  the 
ion  with  which  the  protein  is  in  combination.  Thus  by  adding 
K2SC>4  to  a  solution  of  gelatin  chloride,  gelatin  sulphate  is  formed 
resulting  in  a  diminution  of  osmotic  pressure,  viscosity,  etc.,  of  the 
protein  solution;  or  if  KC1  is  added  to  gelatin  sulphate  the  reverse 
chemical  and  physical  changes  take  place.  If  the  protein  is  on 
the  alkaline  side  of  its  isoelectric  point,  e.g.,  in  the  case  of  Na 
gelatinate,  the  addition  of  a  salt  with  bivalent  cation,  e.g., 
MgCl2  or  CaCl2,  etc.,  results  in  the  formation  of  Mg  or  Ca 
gelatinate  with  the  consequence  that  the  osmotic  pressure,  vis- 
cosity, and  swelling  of  the  gelatin  is  diminished.  By  mixing 
two  different  salts,  e.g.,  NaCl  and  MgCh,  the  antagonistic  effects 
so  well  known  in  biology  can  be  imitated. 

The  second  effect  of  the  addition  of  a  neutral  salt  to  a  solution 
of  a  protein  is  a  general  depressing  effect  on  the  physical  proper- 
ties of  a  solution  of  a  protein  salt  and  this  depression  is  caused 
by  that  ion  of  the  salt  which  has  the  opposite  sign  of  charge  to 
that  of  the  protein  ion.  Thus  all  anions  regardless  of  valency 
depress  the  osmotic  pressure,  viscosity,  and  swelling  of  gelatin 
chloride  and  the  depressing  effect  increases  with  the  concentra- 
tion and  valency  of  the  anion  of  the  salt  added.  All  cations 
depress  the  viscosity,  swelling,  and  osmotic  pressure  of  Na  gela- 
tinate and  the  more  so  the  higher  the  concentration  and  valency 
of  the  cations  added. 

This  effect  is  similar  to  the  depression  of  electrolytic  dissocia- 
tion of  one  electrolyte  caused  by  the  addition  of  a  second  electro- 
lyte with  a  common  ion,  but,  nevertheless,  the  salt  effects  just 
mentioned  are  not  (or  only  to  a  negligible  degree)  due  to  a  depres- 
sion of  the  degree  of  electrolytic  dissociation  of  the  protein  salt, 
but  are  due  to  Donnan's  membrane  equilibrium. 

Previous  authors  had  already  observed  that  only  electrolytes 
have  a  depressing  effect  on  the  physical  properties  of  protein 


THE  ACTION  OF  NEUTRAL  SALTS 


109 


solutions,  such  as  osmotic  pressure,  viscosity,  etc.,  while  non- 
electrolytes,  like  cane  sugar,  have  no  such  effect.  Since  in  these 
older  experiments  the  pH  was  not  considered  and  since  this  fact 
is  of  paramount  importance,  it  seemed  desirable  to  repeat  them. 
It  was  found  that  non-electrolytes,  like  cane  sugar,  have  no 
depressing  effect  on  the  osmotic  pressure  or  the  viscosity  of  gelatin 
solutions.  Solutions  of  gelatin  chloride  of  pH  3.4  containing  1  gm. 
of  originally  isoelectric  gelatin  in  100  cc.  solution  were  made  up  in 
various  concentrations  of  cane  sugar,  were  rapidly  heated  to  45° 
and  rapidly  cooled  to  24°.  The  time  of  outflow  of  the  gelatin 
solutions  through  a  viscometer  was  measured  immediately.  In 
addition  the  time  of  outflow  of  the  pure  sugar  solution  was  also 
determined  at  24°C.  The  ratio  of  the  time  of  outflow  of  the 
gelatin-cane  sugar  solution  divided  by  the  time  of  outflow  of  the 
pure  cane  sugar  solution  was  thus  determined.  The  results  given 
in  Table  IX  show  that  the  ratio  of  viscosity  of  gelatin  solution  to 
viscosity  of  cane  sugar  solution  is  not  diminished  by  the  addition 
of  cane  sugar;  in  fact  it  seems,  if  anything,  slightly  increased  if 
the  cane  sugar  concentration  is  above  M/8. 

TABLE  IX. — INFLUENCE  OF  THE  ADDITION  OF  CANE  SUGAR  ON  THE  VISCOSITY 

AND  OSMOTIC  PRESSURE  OF  1  PER  CENT  SOLUTIONS  OF  GELATIN 

CHLORIDE  OF  pH  3.4 


Concentration  of  cane  sugar 

N 

<N 

CO 

GO 

r-T 

iO 

3 

eo 

co 

oo 

TH 

<N 

0 

s 

s 

% 

s 

s 

S 

s 

s 

s 

s 

Viscosity  ratio  

2.33 

2.31 

2.33 

2.35 

2.30 

2.31 

2.31 

2.30 

2.39 

2.44 

2.57 

Osmotic     pressure 

after  21  hours  at 

24°C.    in    milli- 

meters H«O  .... 

434 

390 

380 

405 

408 

400 

407 

432 

397 

401 

395 

Similar  results  were  obtained  in  regard  to  osmotic  pressure  as 
Table  IX  shows. 

This  fact  is  one  of  the  prerequisites  for  the  validity  of  the 
theory  of  membrane  equilibrium,  since  only  ions  contribute  to 
the  equilibrium  conditions  on  opposite  sides  of  the  membrane. 

A  second  prerequisite  is,  that  the  addition  of  salts  should  have 


110  THEORY  OF  COLLOIDAL  BEHAVIOR 

no  influence  on  the  viscosity,  osmotic  pressure,  or  P.D.  of  protein 
solutions  at  the  isoelectric  point.  This  prerequisite  of  the 
Donnan  theory  was  also  fulfilled. 

In  his  book  on  "Applied  Colloid  Chemistry"  Bancroft  makes 
the  following  comment  on  the  writer's  experiments  on  the  Hof- 
meister  series. 

"Under  the  conditions  of  the  experiments  Loeb  found  that  on  the  acid 
side  of  the  isoelectric  point  only  anions  of  neutral  salts  are  taken  up  and  on 
the  alkaline  side  of  the  isoelectric  point  only  cations.  Since  the  Hofmeister 
series  calls  for  an  effect  due  to  both  ions  of  a  neutral  salt  on  the  swelling  of 
gelatine,  Loeb  concludes  that  the  Hofmeister  series  is  a  delusion  and  a  snare. 
This  does  not  follow  at  all.  Loeb  is  working  at  such  extreme  dilutions  that 
the  specific  effects  of  all  ions  but  hydrogen  and  hydroxyl  ions  are  practically 
negligible.  In  acid  solutions  only  anions  are  taken  up  and  in  alkaline 
solutions  only  cations.  Loeb  recognizes  the  specific  effect  of  iodine  ions  over 
chlorine  ions  in  causing  the  liquefaction  of  gelatine;  but  he  considers  that 
liquefaction  stands  in  no  necessary  relation  to  swelling,  an  assumption  which 
will  be  shared  by  few.  With  higher  salt  concentrations  Loeb  will  undoubt- 
edly get  entirely  different  results."1 

The  answer  to  this  comment  is  that  when  Bancroft  wrote  it  he 
had  not  read  the  writer's  later  papers  dealing  with  the  Hof- 
meister series.  A  glance  at  Figs.  27,  29,  30,  31,  33,  35,  46,  and  60 
will  show  that  salt  solutions  up  to  grammolecular  concentration 
were  used  without  any  indication  of  the  validity  of  the  Hof- 
meister series  being  found.  Bancroft  will  surely  not  maintain 
that  solutions  of  neutral  salts  up  to  molecular  concentration  are 
so  dilute  that  the  effects  of  all  ions  except  the  hydrogen  and 
hydroxyl  ions  are  practically  negligible. 

The  writer's  statement  that  the  liquefaction  of  solid  gelatin 
stands  in  no  necessary  relation  to  swelling  is  correct,  since  higher 
concentrations  of  acids  or  of  salts  like  CaCl2  diminish  the  swelling 
of  gelatin  while  they  increase  its  solubility  (see  Chap.  XIV). 
This  is  due  to  the  fact  that  swelling  and  solution  of  solid  gelatin 
in  the  presence  of  acid  are  functions  of  different  variables,  swell- 
ing in  acid  depending  on  the  Donnan  equilibrium,  while  the  solu- 
tion of  gelatin  depends  on  the  same  forces  which  are  responsible 
for  the  solution  of  ordinary  crystalloids  in  water  (probably 
secondary  valency  forces). 

The  belief  in  the  validity  of  the  Hofmeister  series  has  given  rise 

1  BANCROFT,  W.  D.,  "Applied  Colloid  Chemistry,"  New  York  and  London, 
1921,  pp.  255-256. 


THE  ACTION  OF  NEUTRAL  SALTS  111 

to  a  flood  of  speculations  concerning  the  nature  of  physiological 
and  pathological  processes.  These  speculations  were,  unfortu- 
nately, rarely  supported  by  adequate  experimntes  and  when  experi- 
ments •  were  made  the  hydrogen  ion  concentrations  were  ignored, 
so  that  the  basis  of  these  speculations  is  always  uncertain  if  not 
positively  wrong.  Thus  it  has  been  suggested  that  muscular 
contraction  is  due  to  swelling  caused  by  acid  formation.  This 
may  or  may  not  turn  out  to  be  correct,  but  the  production  of 
acid  in  the  muscle  can  only  lead  to  increased  swelling  if  the  pH 
inside  the  muscle  is  lower  (but  not  much  lower)  than  that  of  the 
isoelectric  point  of  the  proteins  responsible  for  the  alleged  swell- 
ing; since  otherwise  the  acid  formation  could  only  diminish  the 
swelling  already  existing  in  the  resting  muscle.  It  is  obvious 
that  we  must  know  the  isoelectric  points  of  the  proteins  in  the 
muscle,  as  well  as  the  pH  in  the  resting  and  the  active  muscle, 
before  a  discussion  of  the  hypothesis  becomes  profitable. 

It  has  been  stated  that  edema  is  due  to  the  swelling  of  proteins 
inside  the  cells  caused  by  acid  formation.  Not  only  have  none 
of  the  measurements  of  the  hydrogen  ion  concentrations  required 
for  such  a  hypothesis  been  made  but  all  critical  experiments  and 
clinical  observations  indicate  that  edema  is  a  phenomenon 
dependent  on  increased  filtration  of  liquid  from  the  capillaries 
into  the  spaces  between  tissues  or  cells;  while  there  is  no  indica- 
tion that  edema  is  connected  with  colloidal  swelling.1 

It  has  been  suggested  that  the  absorption  of  water  by  the 
striped  muscle  (and  by  other  cells)  in  hypotonic  solutions  is  due 
to  a  colloidal  swelling  caused  by  acid  formation  inside  the  cells, 
but  it  can  be  shown  that  if  the  solution  is  rendered  isotonic  by 
the  addition  of  a  sugar,  the  living  muscle  no  longer  absorbs 
water.2  This  proves  that  the  absorption  of  water  by  living 
muscles  (and  other  living  cells)  in  hypotonic  solution  is  due  to 
the  fact  that  these  tissues  or  cells  are  surrounded  by  semiper- 
meable  membranes  and  that  the  absorption  of  water  by  living 
striped  muscles  or  cells  in  hypotonic  solutions  has  no  connection 
with  colloidal  swelling. 

1  See  HIRSCHFELDER,  A.  D.,  Trans.  Section  Pharmacol.  and  Therapeutics, 
Am.  Med.  Assoc.,  p.  182,  1917;  and  MOORE,  A.  R.,  Am.  J.  Physiol,  vol.  37, 
p.  220,  1915. 

2  HOBER,  R.,  " Physikalische  Chemie  der  Zelle  und  der  Gewebe,"  p.  386, 
Leipsic  and  Berlin,  1914.     LOEB,  J.,  Science,  vol.  37,  p.  427,  1913. 


CHAPTER  VII 

THE  INADEQUACY  OF  THE  PRESENT  THEORIES  OF 
COLLOIDAL  BEHAVIOR 

We  have  given  a  survey  of  the  influence  of  electrolytes  on  the 
behavior  of  proteins  and  we  may  now  single  out  those  character- 
istics which  are  specifically  colloidal,  i.e.,  which  do  not  seem  to 
occur  in  crystalloids.  These  characteristics  are: 

1.  The  addition  of  little  acid  (or  alkali)  to  an  isoelectric  protein 
(crystalline  egg  albumin,  gelatin,  and  casein)  increases,  and  the 
addition  of  more  acid  (or  alkali)  diminishes  the  osmotic  pressure, 
the  viscosity  (and  also,  as  will  be  seen,  the  potential  differences)  of 
solutions  of  these  proteins;  and  the  same  is  true  for  the  swelling 
of  gelatin. 

2.  This  effect  of  acids  and  alkalies  depends  only  on  the  sign 
and  the  valency  of  the  ions  in  combination  with  the  proteins; 
ions  of  the  same  sign  and  valency,  e.g.,  Cl,  NO3,   CH3COO, 
H2PO4  HC2O4  etc.,  influence  the  properties  in  the  same  way, 
provided  that  th,e  properties  of  the  protein  solutions  are  com- 
pared for  the  same  pH  and  the  same  concentration  of  originally 
isoelectric  protein,  and  provided  that  no  constitutional  changes 
occur  in  the  protein  molecule  or  ion. 

3.  When  the  ion  in  combination  with  a  protein  is  bivalent 
(e.g.,  864,  Ca,  Ba)  the  osmotic  pressure,  viscosity,  and  swelling 
of  the  protein  are  considerably  less  than  when  the  ion  is  monova- 
lent  (e.g.,  Cl,  Br,  NO3,  H2PO4,  HC2O4,  Na,  K,  etc.). 

4.  The  addition  of  a  neutral  salt  to  a  protein  solution  (which  is 
not  at  the  isoelectric   point)    depresses  the  osmotic  pressure, 
viscosity  (and  P.D.)  of  the  solutions  and  the  degree  of  swelling 
of  gels,  and  this  effect  increases  with  the  valency  of  that  ion  of 
the  salt  which  has  the  opposite  sign  of  charge  to  that  of  the 
protein  ion. 

Any  theory  which  claims  to  be  able  to  explain  colloidal  behavior 
must  account  quantitatively  for  these  four  results.  As  a  matter 

112 


THEORIES  OF  COLLOIDAL  BEHAVIOR  113 

of  fact  the  explanations  offered  in  the  colloidal  literature  do  not 
even  suffice  as  qualitative  explanations  since  they  are  in  contra- 
diction with  the  facts. 

We  have  seen  in  the  introduction  how  the  original  definition 
of  colloids  by  Graham,  based  on  the  non-diffusion  of  colloids 
(through  membranes),  has  of  late  been  abandoned  by  colloid 
chemists  in  favor  of  the  micella  or  aggregation  theory  of  colloids, 
according  to  which  the  ultimate  unit  of  colloidal  matter  in 
solution  or  suspension  is  not  the  isolated  molecule  or  ion,  but 
an  aggregate  of  the  latter — the  micella  of  Naegeli.  Such  aggre- 
gations occur  and  they  play  a  role  in  gel  formation,  precipitation, 
and  to  some  extent  in  the  viscosity  of  protein  solutions,  but  they 
cannot  explain  the  influence  of  electrolytes  on  the  properties  of 
proteins  mentioned,  since  they  have  only  an  indirect  connection 
with  colloidal  behavior.  It  will  be  shown  that  the  aggregates 
act  like  membranes  blocking  the  diffusion  of  the  ions  constituting 
the  aggregate  and  this  prevention  of  diffusion  is  a  source  of 
colloidal  behavior. 

The  depressing  effect  of  the  addition  of  salts  to  protein  solu- 
tions cannot  be  harmonized  with  the  aggregation  theory.  Zsig- 
mondy  suggests  that  the  depressing  effect  of  a  neutral  salt  on  the 
osmotic  pressure  of  a  solution  of  a  gelatin  salt  might  find  its 
explanation  in  the  assumption  that  the  addition  of  salt  increases 
the  degree  of  aggregation  and  hence  diminishes  the  number 
of  the  particles  in  solution,  the  diminution  in  the  number  of 
particles  leading  to  the  lowering  of  osmotic  pressure.1  It  is 
undoubtedly  true  that  salts  precipitate  proteins  and  that  pre- 
cipitation is  due  to  an  increase  in  aggregation,  but  the  salting 
out  of  gelatin  from  its  watery  solution  is  not  determined  by  the 
ion  with  the  opposite  sign  of  charge  to  that  of  the  protein  ion, 
while  we  have  seen  that  the  depressing  effect  of  a  salt  on  the 
osmotic  pressure  of  gelatin  solutions  is  determined  by  the  ion 
with  the  opposite  sign  of  charge  to  that  of  the  protein  ion.  In 
other  words,  the  salting  out  of  gelatin  from  its  watery  solution 
is  a  process  of  an  entirely  different  character  from  the  lowering 
of  the  osmotic  pressure  of  a  protein  solution  by  a  neutral  salt. 
It  is,  therefore,  impossible  to  explain  the  latter  process  by  the 
former. 

1  ZSIQMONDY,  R.,  "Kolloidchemie,"  2nd  ed,,  p.  342,  Leipsic,  1918, 
8 


114  THEORY  OF  COLLOIDAL  BEHAVIOR 

Moreover,  the  attempt  to  explain  the  depressing  effect  of  the 
addition  of  salts  on  the  basis  of  the  micella  theory  fails  com- 
pletely in  the  case  of  the  other  properties  of  protein  solutions 
which  are  equally  depressed  by  them  as  the  osmotic  pressure, 
namely,  the  viscosity  and  the  P.D. 

We  shall  see  in  Chap.  XIII  that  if  the  state  of  aggregation 
increases  in  a  gelatin  solution — i.e.,  if  isolated  protein  molecules 
or  ions  unite  to  form  a  larger  aggregate — the  viscosity  of  the 
solution  is  thereby  increased,  for  the  reason  that  these  aggregates 
occlude  comparatively  large  quantities  of  water  whereby  the 
relative  volume  occupied  by  the  gelatin  in  the  solution  is  increased. 
This  increase  in  the  volume  of  the  micellae  at  the  expense  of 
water  leads,  as  will  be  seen,  to  an  increase  in  viscosity.  Hence, 
if  we  assume  that  the  addition  of  a  salt  increases  the  degree  of 
aggregation  in  protein  solution,  it  would  follow  that  this  should 
result  in  an  increase  of  viscosity;  while  the  addition  of  salt 
depresses  the  viscosity.  The  attempt  to  explain  the  depressing 
influence  of  salts  on  the  osmotic  pressure  and  viscosity  of  protein 
solutions  on  the  basis  of  the  aggregation  theory  leads  therefore 
to  conclusions  which  are  in  contradiction  with  the  actual  facts. 

An  attempt  to  account  for  the  colloidal  behavior  of  protein 
solutions  was  made  by  Pauli  in  his  theory  of  hydration  of  protein 
ions. 

Kohlrausch  had  tried  to  account  for  the  differences  in  the 
mobility  of  different  ions  by  the  assumption  that  each  ion  is 
surrounded  by  a  shell  of  water  and  that  the  velocity  of  migration 
of  ions  is  greatest  where  this  shell  of  water  is  a  minimum.  Pauli 
assumes  that  the  protein  ion  is  surrounded  by  an  enormous 
shell  of  water  while  no  such  jacket  of  water  surrounds  the 
non-ionized  protein.1  The  shell  of  water  might  prevent  the  coa- 
lescence of  the  protein  ions  and,  hence,  might  cause  a  higher 
degree  of  dispersion.  On  the  basis  of  the  hydration  theory  we 
can  find  a  qualitative  explanation  of  the  peculiar  pH  curves  in  the 
following  way :  At  the  isoelectric  point  protein  is  in  a  non-ionized 
condition  and  no  hydration  occurs.  Hence,  the  degree  of  disper- 
sion of  particles  and  the  osmotic  pressure  are  a  minimum  at  this 
point  and  the  viscosity  and  swelling  should  also  be  a  minimum, 

1  PAULI,  W.,  Fortschr.  naturwiss.  Forschung,  vol.  4,  p.  223,  1912,  "Kol- 
loidchemie  der  Eiweisskorper,"  Dresden  and  Leipsic,  1920, 


THEORIES  OF  COLLOIDAL  BEHAVIOR 


115 


since  swelling  might  be  directly  due  to  the  existence  of  this  water 
jacket,  and  viscosity  should  also  increase  with  the  mass  of  water 
surrounding  each  particle.  If  an  acid,  e.g.,  HC1,  is  added  to 
isoelectric  gelatin,  the  latter  will  be  transformed  into  gelatin 
chloride  which,  being  a  salt,  is  strongly  dissociated.  The  more 
acid  is  added  the  more  gelatin  is  transformed  into  gelatin  chloride. 
We  have  shown  in  Chap.  V  that  the  curves  for  osmotic  pres- 
sure, swelling,  and  viscosity  reach  a  maximum  at  a  pH  varying 
between  3.5  and  2.8,  and  that  they  then  drop.  Pauli  assumes 
that  the  drop  is  due  to  a  repression  of  the  degree  of  electrolytic 
dissociation  of  the  gelatin  chloride  (or  any  protein-acid  salt) 
through  the  addition  of  more  acid  on  account  of  the  common 
anion.  It  should,  however,  be  mentioned  that  Pauli1  and 
Manabe  and  Matula2  state  that  the  maximum  of  the  curves 
occurs  not  at  pH  between  3.5  or  pH  2.8,  but  at  pH  2.1  or  2.0. 
Table  X  shows  that  the  pH  for  the  maximal  values  of  the 
physical  properties  of  gelatin,  crystalline  egg  albumin,  and 
casein  solutions  is  considerably  higher  than  2.1.  In  fact  at  a 
pH  of  2.1  the  osmotic  pressure  of  gelatin  chloride  and  albumin 
chloride  solutions  is  half  way  down  between  that  at  the  maxi- 
mum (pH  3.4)  and  at  the  minimum  (the  isoelectric  point, 
pH  4.7). 

TABLE  X 


1  per  cent  protein  chloride 
solution 

pH  where  the  maximal  values  are 
observed  for 

Osmotic  pressure 

Swelling 

Viscosity 

Gelatin  

3.4 
3.4 
3.0 

3.2 

2.9 
3.0 

Crystalline  egg  albumin  

Casein  

The  assumption  that  the  maximum  lies  at  pH  2.1,  therefore, 
does  not  agree  with  the  observations  made  on  the  physical 
behavior  of  the  three  proteins  mentioned  in  Table  X.  It  might 
be  true  for  the  viscosity  of  solutions  of  blood  albumin,  on  which 

1  PAULI,  W.,  "  Kolloidchemie  der  Eiweisskorper,"  Dresden  and  Leipsic, 
1920. 

2  MANABE,  K.  and  MATULA,  J.,  Biochem.  Z.,  vol.  53,  p.  369,  1913. 


116  THEORY  OF  COLLOIDAL  BEHAVIOR 

Pauli  has  done  most  of  his  work,  but  Michaelis  and  Mostynski1 
have  pointed  out  that  there  is  no  maximum  of  viscosity  in  the  case 
of  serum  albumin.  There  is  also  no  maximum  in  viscosity 
followed  by  a  drop  in  the  case  of  egg  albumin  when  the  pH  varies. 

The  hydration  hypothesis  can  be  put  to  a  direct  test  by  deter- 
mining the  specific  conductivity  of  solutions  of  protein  salts,  e.g., 
gelatin  chloride,  albumin  chloride,  etc.  Since  according  to  the 
hydration  hypothesis  only  the  protein  ion  undergoes  hydration, 
the  variation  in  the  osmotic  pressure,  swelling,  and  viscosity 
should  be  accompanied  by  a  corresponding  variation  in  the 
concentration  of  protein  ions  in  solution.  If,  therefore,  the 
specific  conductivity  of  gelatin  chloride  is  measured  at  varying 
pH  but  equal  concentrations  of  originally  isoelectric  gelatin,  the 
curves  representing  the  values  found  for  conductivity  of  the 
protein  should  run  parallel  with  the  curves  for  the  osmotic 
pressure,  swelling,  and  viscosity;  moreover,  the  curve  for  the 
conductivity  of  gelatin  sulphate  should  be  only  about  half  as  high 
as  the  curve  for  the  specific  conductivity  of  gelatin  chloride; 
while  the  curve  for  the  specific  conductivity  of  gelatin  oxalate 
should  be  almost  but  not  quite  as  high  as  that  for  gelatin  chloride. 
The  experiments  show  that  this  is  not  the  case. 

The  concentration  of  ionized  gelatin  in  solution  can  be  deter- 
mined with  the  aid  of  conductivity  measurements  of  the  solution 
of  a  gelatin  salt,  e.g.,  gelatin  chloride,  by  deducting  the  conduc- 
tivity of  the  free  HC1  in  the  solution  from  the  total  conductivity 
of  the  gelatin  solution,  since  the  gelatin  chloride  solution  prepared 
by  the  writer's  method  from  washed  powdered  isoelectric  gelatin 
contains  practically  no  other  electrolyte  except  the  free  HC1  and 
the  gelatin  chloride.  This  was  proved  by  ash  determinations 
and  by  the  fact  that  a  solution  of  isoelectric  gelatin  prepared 
according  to  our  method  of  washing  has  practically  a  con- 
ductivity of  zero.  The  method  of  procedure  was  as  follows: 

Solutions  of  different  gelatin-acid  salts  were  prepared  in  two 
different  concentrations  of  originally  isoelectric  gelatin,  0.8  per 
cent  and  2.4  per  cent.  The  specific  conductivities  of  these  gelatin- 
acid  salts  were  determined  at  different  pH.  The  conductivities 
of  pure  aqueous  solutions  of  the  same  acids  at  different  pH  were 
also  measured.  In  both  cases  the  conductivities  were  plotted 

1  MICHAELIS,  L.  and  MOSTYNSKI,  B.,  Biochem.  Z.,  vol.  25,  p.  401,  1910. 


THEORIES  OF  COLLOIDAL  BEHAVIOR 


117 


as  ordinates  over  the  pH  as  abscissae.  By  deducting  the  values  for 
the  specific  conductivity  of  the  pure  aqueous  solution  of  an  acid 
from  the  values  for  the  total  specific  conductivity  of  the  gelatin- 
acid  solution  of  the  same  pH  the  curve  for  the  specific  conduc- 
tivity of  the  gelatin-acid  salt  for  that  pH  is  obtained.1 

Figure  38  shows  that  the  curves  representing  the  percentage 
of  ionized  gelatin  in  gelatin  chloride  resemble  the  combination 


2.0   22   2A  26  2£>  3.0  32  3.4  3.6  3.8  4.0  42   4.4  4.6 


FIG.  38.  —  Curves  for  the  specific  conductivity  of  2A  per  cent  solutions  of 
gelatin  chloride,  sulphate,  and  oxalate,  showing  the  entirely  different  character  of 
these  curves  from  that  of  the  osmotic  pressure  curves  in  Figs.  14  and  15. 

curves  in  Fig.  8,  since  in  both  cases  there  is  a  gradual  rise  in  the 
concentration  of  ionizable  protein  at  a  pH  below  that  of  the 
isoelectric  point,  but  no  maximum  followed  by  a  drop  at  pH  3.4  or 
3.0.  But  otherwise  the  curves  for  combination  and  for  con- 
ductivity differ;  the  curve  representing  the  percentage  of  ionized 
gelatin  is  almost  the  same  for  gelatin  chloride  and  gelatin  sulphate, 
while  for  gelatin  oxalate  the  curve  is  a  little  lower.  If  we  attempt 
1  LOEB,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  247,  1920-21. 


118 


THEORY  OF  COLLOIDAL  BEHAVIOR 


to  account  for  the  low  osmotic  pressure  of  gelatin  sulphate  solutions 
by  the  hydration  hypothesis,  the  specific  conductivity  of  gelatin 
sulphate  should  be  half  or  less  than  half  of  that  of  gelatin  chloride, 
while  the  curve  for  gelatin  oxalate  should  be  almost  as  high  as 
that  for  gelatin  chloride.  Figure  38  shows  that  neither  expec- 
tation is  fulfilled. 


\ 


50 


PH  20  22  Z4  26   2.6  3.0  3.2  3.4  3.6  3.8  4.0  42  4.4  4.6  46  5.Q 
FIG.  39. — Comparison  of  conductivity  curve  and  osmotic,  pressure  curve  for 
albumin  chloride,  showing  the  entirely  different  character  of  the  two  curves. 

Figure  39  shows  that  the  same  disagreement  exists  between  the 
conductivity  curve  and  the  osmotic  pressure  curve  for  solutions 
of  the  chloride  of  crystalline  egg  albumin.  These  curves,  then, 
do  not  support  the  hydration  hypothesis. 

Pauli's  hydration  theory  rests,  as  stated  above,  on  an  assump- 
tion made  by  Kohlrausch  that  the  difference  in  the  mobility  of  ions 
is  due  to  molecules  of  water  being  dragged  along  with  the  migrat- 
ing ion.  Lorenz,1  Born,2  and  others  have  come  to  the  conclusion 
that  while  Kohlrausch's  idea  is  probably  correct  for  monatomic 
ions  it  cannot  be  correct  for  large  polyatomic  ions.  This  would 

1  LORENZ,  R.,  Z.  Elektrochem.,  vol.  26,  p.  424,  1920. 

2  BORN,  M.,  Z.  Elektrochem.,  vol.  26,  p.  401,  1920. 


THEORIES  OF  COLLOIDAL  BEHAVIOR  119 

exclude  the  assumption  of  a  high  degree  of  hydration  of  protein 
ions. 

The  theory  of  adsorption  is  used  to  explain  the  precipitation  of 
colloids  by  low  concentrations  of  salts.  The  experiments  de- 
scribed in  the  second,  third,  and  fourth  chapters  of  this  book  flatly 
contradict  the  assumption  of  such  an  adsorption  when  the  con- 
centration of  salts  is  low. 

The  adsorption  theory,  the  aggregate  theory,  and  the  hydration 
theory  cannot  explain  the  features  of  colloidal  behavior  enu- 
merated at  the  beginning  of  this  chapter. 

As  long  as  chemists  continue  to  believe  in  the  applicability 
of  the  adsorption  formula  to  the  behavior  of  proteins,  no  scientific 
theory  of  colloidal  behavior  will  be  possible.  We  intend  to  show 
in  the  second  part  of  the  book  that  such  a  theory  can  be  given  on 
the  basis  of  the  stoichiometrical  proof  that  proteins  form  true 
salts  with  acids  and  alkalies,  and  that  these  salts  lead  to  the 
formation  of  protein  ions.  Colloidal  behavior  is  due  to  the  fact 
that  these  protein  ions  cannot  diffuse  through  many  membranes 
which  are  permeable  to  the  majority  of  crystalloidal  ions,  or  that 
protein  ions  form  solid  gels  in  which  cohesive  forces  prevent  their 
diffusion,  while  such  gels  are  permeable  to  crystalloidal  ions.  The 
theory  of  the  equilibrium  conditions  resulting  from  this  difference 
in  the  diffusibility  of  the  two  opposite  ions  of  an  electrolyte  was 
developed  by  Donnan.  These  equilibrium  conditions  give  rise 
to  forces,  such  as  P.D.,  osmotic  pressure,  etc.,  which  are  the  only 
cause  of  colloidal  behavior.  It  will  be  shown  that  Donnan's 
theory  gives  not  only  a  qualitative  but  a  quantitative  and 
mathematical  explanation  of  colloidal  behavior. 


CHAPTER  VIII 
MEMBRANE  POTENTIALS1 

We  have  seen  that  electrolytes  influence  the  osmotic  pressure, 
swelling,  and  viscosity  of  protein  solutions  in  a  similar  way,  so 
that  we  must  think  of  the  possibility  that  the  cause  of  this  influ- 
ence is  the  same  for  all  these  properties. 

When  a  solution  of  a  protein  salt,  e.g.,  I  per  cent  gelatin 
chloride,  is  separated  from  distilled  water  by  a  collodion  mem- 
brane, a  potential  difference  exists  across  the  membrane  between 
the  gelatin  chloride  solution  and  the  outside  solution  with  which 
it  is  in  equilibrium.  If  this  P.D.  is  measured  with  the  aid  of  a 
Compton  electrometer  with  saturated  KC1  calomel  electrodes, 
it  is  found  that  the  P.D.  is  influenced  in  the  same  way  by 
electrolytes  as  the  osmotic  pressure,  swelling,  and  viscosity  (see 
Fig.  41  in  this  chapter).  This  in  itself  would  only  mean  the 
addition  of  another  property  varying  in  the  same  characteristic 
way  as  osmotic  pressure,  or  swelling,  or  viscosity  of  proteins 
under  the  influence  of  electrolytes,  if  it  were  not  for  the  fact  that 
we  can  correlate  the  variations  of  the  new  property  with  the 
Donnan  equilibrium,  and  that  we  can  calculate  the  P.D.  with  a 
fair  degree  of  accuracy  on  the  basis  of  this  equilibrium.  This 
then  gives  us  a  rational,  quantitative  theory  of  the  influence  of 
the  pH,  the  valency  of  ions,  and  of  the  concentration  of  neutral 
salts  on  a  colloidal  property  of  proteins. 

It  is  necessary  to.  give  a  brief  description  of  the  method  of 
measuring  the  P.D.  Suppose  that  the  protein  in  solution  is 
gelatin  chloride  containing  1  gm.  of  originally  isoelectric  gelatin 
in  100  c.c.  solution.  Such  solutions  of  gelatin  chloride  are  put 
into  collodion  bags  closed  with  rubber  stoppers  which  are  per- 
forated with  glass  tubes  serving  as  manometers,  as  described  in 
the  osmotic  pressure  experiments.  These  collodion  bags  filled 

1  This  chapter  is  based  on  LOEB,  J.,  J.  Gen.  Physiol,  vol.  3,  pp.  557,  667, 
1920-21;  vol.  4,  pp,  351,  463,  1921-22. 

120 


MEMBRANE  POTENTIALS 


121 


with  the  gelatin  chloride  solution  are  dipped  into  beakers  con- 
taining 350  c.c.  of  aqueous  HC1  solution  of  originally  the  same 
pH  as  that  of  the  gelatin  chloride  solution,  but  free  from  gelatin. 
The  experiments  last  20  hours  or  more  at  24°C.  to  allow  the 
establishment  of  osmotic  equilibrium  between  the  two  solutions 
(which  requires  only  about  6  hours  under  the  conditions  of  the 
experiments).  After  20  hours  or  more  the  P.D.  between  the 
gelatin  solution  (which  we  call  the  inside  solution)  and  the  aqueous 


FIG.  40. — Method  of  measuring  the  P.D.  between  gelatin  chloride  solution  in  a 
collodion  bag  and  the  outside  HC1  solution  in  beaker. 

solution  (which  we  call  the  outside  solution)  is  measured  with  the 
aid  of  a  Compton  electrometer,  giving  a  deviation  of  about  2 
mm.  on  the  scale  for  1  millivolt  at  a  distance  of  about  2  m.  The 
two  electrodes  leading  to  the  electrometer  are  identical  (Fig.  40). 
They  are  calomel  electrodes  filled  with  saturated  KC1  solution. 
One  electrode  dips  through  a  capillary  glass  tube  into  the  gelatin 
solution,  the  other  also  through  a  capillary  glass  tube  into  the 
outside  solution.  In  order  to  allow  the  electrode  to  dip  into  the 
gelatin  solution,  the  glass  tube  serving  as  a  manometer  is  replaced 
by  a  funnel,  as  shown  in  the  figure.  In  the  figure  the  upper  level 


122 


THEORY  OF  COLLOIDAL  BEHAVIOR 


of  the  gelatin  solution  is  in  the  funnel.  This  is  not  really  neces- 
sary but  it  is  convenient  and  is  accomplished  by  allowing  the 
collodion  bag  to  press  against  the  glass  wall  of  the  beaker  con- 


1.8    2.0  22  24   26   28  3.0   3.2  3.4   3.6  3.8  40  42  4.4  46  4.8 


Fia.  41.  —  Influence  of  pH  and  valency  of  anion  on  P.D.  of  solutions  of  different 
gelatin-acid  salts.  The  curves  in  Fig.  41  are  similar  to  (but  not  identical  with) 
those  in  Fig.  14. 


taining  the  outside  solution.  As  a  minor  but  convenient  acces- 
sory each  electrode  is  connected  with  a  reservoir  of  saturated 
KC1  solution  which  makes  it  possible  to  let  the  KC1  solution  in 
the  capillary  flow  out  after  each  measurement,  so  that  the 
electrode  is  always  clean  for  each  new  measurement.  What  was 


MEMBRANE  POTENTIALS 


123 


measured  in  this  way  was,  therefore,  the  electromotive  force 
of  the  following  cell, 


calomel 
electrode 

saturated 
KC1 

outside 
solution 
HC1 

collodion 
mem- 
brane 

inside 
solution 
gelatin 
chloride 

saturated 
KC1 

calomel 
electrode 

It  is  found  that  in  this  cell  the  gelatin  solution  has  a  positive 
charge  and  the  outside  solution  a  negative  charge  and  that  the 
P.D.  varies  with  the  pH  of  the  gelatin  chloride  solution,  as  indi- 
cated in  Fig.  41.  It  is  also  found  that  the  P.D.  of  gelatin  phos- 
phate solutions  is  practically  identical  with  the  P.D.  of  gelatin 
chloride  solutions  of  the  same  pH  and  that  both  are  considerably 
higher  (about  50  per  cent  higher,  as  we  shall  see)  than  the  P.D.  of 
gelatin  sulphate  solutions.  We  shall  also  see  that  the  addition 
of  a  neutral  salt  to  the  gelatin  chloride  solution  depresses  the 
P.D.  In  other  words,  electrolytes  influence  the  P.D.  between 
gelatin  chloride  solution  and  outside  solution  in  a  way  similar 
to  that  in  which  they  influence  the  osmotic  pressure  and  the 
viscosity  of  the  same  solution.  It  becomes,  therefore,  of  con- 
siderable importance  to  find  out  the  origin  of  this  P.D.  We 
intend  to  show  that  the  P.D.  is  due  to  the  establishment  of  a 
Donnan  equilibrium  between  the  gelatin  chloride  solution  and  the 
outside  aqueous  solution  (free  from  gelatin). 

We  have  already  given  a  brief  outline  of  Donnan 's  membrane 
theory  in  the  first  chapter.  In  our  experiment  a  collodion  bag 
filled  with  a  1  per  cent  solution  of  gelatin  chloride  is  dipped  into 
a  beaker  containing  a  solution  of  HC1  (without  gelatin)  of  origin- 
ally the  same  pH  as  that  of  the  gelatin  solution.  In  this  case  we 
have  free  HC1  inside  as  well  as  outside,  but  in  addition  we  have 
inside  the  collodion  bag  a  gelatin  chloride  solution  which  ionizes 
into  Cl  and  a  positive  gelatin  ion.  The  gelatin  ion  is  unable  to 
diffuse  through  the  collodion  membrane  but  the  H  ions  and  Cl 
ions  can  diffuse  freely  through  the  membrane.  Donnan  has 
shown  that  in  this  case  an  equilibrium  condition  is  established 
in  which  the  product  of  the  concentrations  of  the  H  and  Cl  ions 
in  the  outside  solution  equals  the  product  of  the  concentrations 
of  the  H  and  Cl  ions  inside.  This  equilibrium  is  expressed  by 


124  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  following  equation,  which  was  used  by  Procter  and  Wilson 
for  the  distribution  of  free  HC1  between  a  jelly  of  solid  gelatin 
chloride  and  surrounding  water,  but  which  holds  also  for  the 
case  where  the  gelatin  chloride  is  in  solution  and  separated  from 
the  outside  solution  by  a  collodion  membrane  impermeable  for 
gelatin  ions, 

x2  =  y(y  +  z)  (1) 

where  x  is  the  concentration  of  H  and  Cl  ions  in  the  outside 
solution,  y  the  concentration  of  the  H  and  Cl  ions  of  the  free 
acid  inside  the  gelatin  solution,  and  .z  the  concentration  of  the 
Cl  ions  in  combination  with  the  gelatin.  (For  the  sake  of 
simplification  complete  electrolytic  dissociation  of  HC1  and 
gelatin  chloride  is  assumed.)  Since  all  the  quantities  in  Equa- 
tion (1)  are  positive,  the  concentration  x  of  the  hydrogen  ions 
in  the  outside  solution  must  be  greater  than  the  concentration  y 
of  the  hydrogen  ions  in  the  inside  solution;  and  the  total  con- 
centration of  the  chlorine  ions  in  the  inside  solution,  y  +  z, 
must  be  greater  than  the  concentration  of  the  Cl  ions  in  the  out- 
side solution,  x.  This  difference  in  the  distribution  of  the 
crystalloidal  ions  on  the  opposite  sides  of  the  membrane  is 
caused  by  the  fact  that  one  type  of  ions  (the  protein  ions)  cannot 
diffuse  through  the  membrane. 

We  now  come  to  the  most  important  point  for  the  foundation 
of  the  theory  of  colloidal  behavior.  If  it  is  true  that  the  Donnan 
equilibrium  is  the  cause  of  the  P.D.  between  a  gelatin  chloride 
solution  and  the  outside  solution,  the  Donnan  equilibrium  is 
likely  to  be  also  the  cause  of  the  influence  of  the  mysterious 
influence  of  electrolytes  on  the  other  properties  of  proteins,  since 
the  curves  for  P.D.  are  similar  to  the  curves  of  osmotic  pressure, 
viscosity,  and  swelling.  In  order  to  prove  that  the  P.D.  is  due 
to  the  Donnan  equilibrium,  we  must  be  able  to  show  that  the 
unequal  distribution  of  the  H  and  Cl  ions  on  the  opposite  sides 
of  the  collodion  membrane  allows  us  to  account  quantitatively 
for  the  P.D.  on  the  basis  of  Nernst's  well  known  logarithmic 
formula  for  concentration  cells. 

We  have  seen  in  Chap.  IV  that  we  can  determine  the  con- 
centration of  the  Cl  ions  of  the  gelatin  chloride  solution  by  titra- 
tion;  and  we  can,  of  course,  also  determine  the  Cl  of  the  outside 
watery  solution  by  titration.  Let  x  be  the  concentration  of  Cl 


MEMBRANE  POTENTIALS  125 

ions  in  the  outside  solution  and  y  +  z  the  concentration  of  Cl  in 
the  gelatin  solution  (as  found  by  titration)  and  let  us  assume  that 
this  difference  of  concentration  determines  the  P.D.  observed 
between  the  gelatin  chloride  solution  and  the  outside  solution, 
then  we  should  expect  that  at  24°C.  the  observed  P.D.  =  .059 

loS  ly~+~z  volts- 

We  shall  see  later  in  this  chapter  that  the  observed  P.D.  in 
millivolts  is  actually  equal  to  59  log  — ^—  millivolts,  and  this 

makes  it  very  probable  that  the  P.D.  between  a  gelatin  chloride 
solution  and  the  outside  watery  solution  across  a  collodion 
membrane  is  caused  exclusively  by  the  Donnan  equilibrium. 

We  have  a  second  check  since  it  follows  also  that  we  must  be 
able  to  calculate  our  observed  P.D.  on  the  basis  of  the  difference 
in  the  concentration  of  hydrogen  ions  on  the  opposite  sides  of  the. 
membrane  with  the  aid  of  Nernst's  formula.  Donnan's  equilib- 
rium equation 

z2  =  y(y  +  z) 
can  be  written  in  the  form 

y  =    x 

x      y  +  z 

where  y  is  the  concentration  of  the  hydrogen  ions  inside  the 
gelatin  solution  and  x  the  concentration  of  the  hydrogen  ions 
in  the  outside  solution.  Hence,  if  the  Donnan  equilibrium  is 
responsible  for  the  observed  P.D.  between  the  gelatin  chloride 
solution  and  the  watery  solution,  it  must  also  be  possible  to 
show  that 

Observed  P.D.  =  59  log  |  millivolts 

We  intend  to  show  that  this  is  actually  the  case.  Instead  of 
measuring  the  concentration  of  the  hydrogen  ions  inside  (i.e., 
in  the  gelatin  solution)  and  outside  (i.e.,  in  the  aqueous  solution) 
by  titration,  we  measure  these  concentrations  with  the  hydrogen 
electrode.  Since  log  y  is  the  value  pH  inside  and  log  x  the  value 
pH  outside,  the  value  59  (pH  inside  minus  pH  outside)  millivolts 
must  (within  the  limits  of  accuracy  of  measurement)  be  equal  to 


126  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  observed  P.D.  if  the  Donnan  equilibrium  is  the  exclusive 
cause  for  the  P.D.  between  a  gelatin  chloride  solution  and  the 
outside  watery  solution;  neglecting  the  sign.1 

Although  the  value  pH  inside  minus  pH  outside  is  an  observed 
value,  e.g.,  observed  with  the  hydrogen  electrode,  we  will  call  the 
value  59  (pH  inside  minus  pH  outside)  the  calculated  P.D.  to 
distinguish  it  from  the  P.D.  observed  with  the  indifferent 
electrodes. 

THE   INFLUENCE   OF  THE   HYDROGEN   ION   CONCENTRATION   OF   GELATIN 
SOLUTIONS  ON  THE  P.D. 

Collodion  bags  of  a  volume  of  about  50  c.c.  were  filled  with  1  per 
cent  solutions  of  gelatin  chloride  of  different  pH.  The  bags  were 
put  into  beakers  containing  each  350  c.c.  of  distilled  water.  To 
hasten  the  establishment  of  equilibrium  between  gelatin  chloride 
solution  and  outside  water  some  HC1  was  added  to  the  latter 
—in  fact  the  pH  of  the  gelatin  and  the  outside  solutions  was 
generally  made  equal  at  the  beginning  of  the  experiment.  The 
collodion  flasks  containing  the  gelatin  solution  were  closed  with 
rubber  stoppers  which  were  perforated  by  glass  tubes  serving  as 
manometers  to  allow  the  measurement  of  the  osmotic  pressure  of 
the  solution.  After  about  6  hours  osmotic  equilibrium  was  com- 
plete but  we  waited,  as  a  rule,  about  18  hours  before  measuring 
the  P.D.  across  the  membrane.  Figure  41  shows  that  the  pH 
influences  the  P.D.  in  a  similar  way  as  it  influences  the  osmotic 
pressure,  swelling,  etc.  Similar  experiments  were  made  with  1 
per  cent  solutions  of  gelatin  phosphate,  -gelatin  oxalate,  and 
gelatin  sulphate,  and  the  curves  are  also  given  in  Fig.  41.  To 
demonstrate  the  similarity  between  the  curves  for  osmotic 

1  The  sign  of  the  observed  P.D.  was  apparently,  but  not  in  reality,  the 
reverse  of  the  sign  of  the  calculated  P.D.  In  the  "observed"  P.D.  the 
membrane  (acting  as  a  hydrogen  electrode)  was  between  the  concentrated 
and  dilute  HC1,  while  in  the  "calculated"  values  the  P.D.  was  obtained, 
from  the  potentiometric  determinations  of  the  pH.  In  this  latter  case  two 
hydrogen  electrodes  were  separated  by  a  concentrated  and  a  dilute  solu- 
tion. The  "observed"  P.D.  was  hence  between  two  solutions  of  different 
concentrations  while  in  the  "calculated"  values  we  measured  the  P.D. 
between  two  electrodes.  In  our  tables  the  apparent  (but  not  real)  reversal 
of  sign  is  corrected. 


MEMBRANE  POTENTIALS  127 

pressure  and  P.D.,  the  osmotic  pressures  were  observed  in  all  the 
experiments  used  for  measuring  the  influence  of  pH  on  the  P.D., 
and  Fig.  14  gives  the  osmotic  pressures.  A  comparison  of  the  two 
figures  for  P.D.  (Fig.  41)  and  for  osmotic  pressure  (Fig.  14)  shows 
the  following  similarities:  Both  sets  of  curves  rise  from  the 
isoelectric  point  with  a  lowering  of  the  pH  until  they  reach  a 
maximum;  this  maximum  is,  however,  not  identical  in  the  two 
cases.  For  the  P.D.  it  varies  between  3.6  and  4.0,  while  for  os- 
motic pressure  it  lies  near  3.5.  With  a  further  fall  in  pH  both 
sets  of  curves  show  approximately  the  same  steep  drop. 

The  second  point  of  similarity  is  the  influence  of  valency.  The 
curves  for  the  P.D.  (Fig.  41)  are  practically  the  same  for  gelatin 
chloride  and  gelatin  phosphate,  and  are  but  slightly  lower  in  the 
case  of  gelatin  oxalate,  while  the  curve  for  the  P.D.  is  considerably 
lower  in  the  case  of  gelatin  sulphate.  The  same  is  true  for  the 
osmotic  pressure  curves  (Fig.  14). 

If  these  characteristic  curves  are  exclusively  determined  by 
Donnan's  membrane  equilibrium  it  should  be  possible  to  show 
that  the  variation  of  the  observed  P.D.  with  pH  is  accompanied 
by  a  parallel  variation  of  the  value  pH  inside  minus  pH  outside 
and  that  the  agreement  between  these  two  sets  of  values  is  as 
perfect  as  the  accuracy  of  the  measurements  permits.  Tables 
XI,  XII,  and  XIII  show  that  this  is  true.  The  upper  two  hori- 
zontal rows  give  the  pH  inside  and  outside,  the  third  horizontal 
row  gives  the  difference,  pH  inside  minus  pH  outside,  and  the 
fourth  row  gives  the  P.D.  calculated  in  millivolts  by  multiplying 
the  values  pH  inside  minus  pH  outside  by  59.  The  last  hori- 
zontal row  gives  the  observed  P.D.  in  millivolts.  The  agree- 
ment between  observed  and  calculated  P.D.  is  sufficiently  close 
to  permit  us  to  say  that  the  characteristic  curves  representing  the 
influence  of  the  pH  on  the  P.D.  are  a  consequence  of  the  Donnan 
equilibrium. 

THE  EXPLANATION  OF  THE  P.D.  CURVE 

Figure  41  shows  that  the  P.D.  of  gelatin-acid  salts  is  a  minimum 
at  the  isoelectric  point,  that  it  rises  rapidly  with  the  increase  in 
the  hydrogen  ion  concentration  until  reaching  a  maximum  at  pH 
about  4.0  to  3.8,  and  then  drops  again  with  a  further  increase  of 


128 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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MEMBRANE  POTENTIALS 


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130  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  hydrogen  ion  concentration.  This  is  the  characteristic  pH 
effect  already  discussed  in  connection  with  viscosity,  osmotic 
pressure,  etc.  Pauli  explained  this  behavior  of  the  viscosity 
curves  on  the  basis  of  ionization  and  hy  drat  ion.  The  hydration 
can  have  no  connection  with  the  P.D.,  but  the  ionization  un- 
questionably has.  Pauli  assumes  that  the  viscosity  rises  with 
increasing  ionization  of  a  protein  salt  and  explains  the  maximum 
and  drop  by  the  repression  of  ionization  of  the  protein  salt  by  the 
anion  of  the  acid  added.  This  latter  explanation  is  plainly 
inadequate  in  our  case,  since  it  would  mean  that  the  electrolytic 
dissociation  of  gelatin  chloride  is  markedly  diminished  by  a 
N/10,000  HC1  solution.  We  can  show  that  the  Donnan  theory 
accounts  mathematically  for  the  influence  of  pH  on  the  P.D.  of 
gelatin  chloride  solutions  as  expressed  in  Fig.  41. 

Donnan  had  arrived  at  his  equilibrium  equation  on  the  basis 
of  thermodynamical  considerations,  but  Proctor  and  Wilson 
have  pointed  out1  that  it  can  be  derived  more  simply  from  the 
ordinary  laws  of  ionization, 

"since  the  nonionized  portion  of  hydrochloric  acid  which,  although  small, 
must  exist  takes  no  direct  part  in  the  equilibrium  and  must  be  equal  in 
both  places.  " 

Hence  when  a  solution  of  gelatin  chloride  is  separated  by  a 
collodion  membrane  from  a  solution  of  HC1  (without  gelatin), 
if  x  is  the  concentration  of  H  and  Cl  ions  in  the  outside  solu- 
tion and  [HC1]  the  concentration  of  non-ionized  HC1, 

x2  =  K  [HC1] 

If  y  is  the  concentration  of  hydrogen  ions  inside  the  solution, 
y  is  the  corresponding  concentration  of  Cl  ions;  and  if  z  is  the 
concentration  of  Cl  ions  in  combination  with  gelatin 

y(y  +  z)  =  K  [HC1] 
hence 

z2  =  y(y  +  z)  (1) 


x  =  V  y(y  +  z) 

PROCTER,  H.  R.,  and  WILSON,  J.  A.,  J.  Chem.  Soc.,  vol.  109,  p.  309,  1916. 


MEMBRANE  POTENTIALS 


131 


Substituting  \/y(y  +  z)  for  x  in  the  term  -  we  get 


Vy(y 


%••&! 


Hence  at  18°C.  the  P.D.  should  be  =  y  log  (l  +  -)  millivolts. 

We  will  now  show  that  from  the  term  \n  +  -  the  influence  of 

y 

pH  on  the  P.D.  as  expressed  in  the  curves  of  Fig.  41  can  be  derived. 

When  we  add  little  HC1  to  isoelectric  gelatin,  we  increase  the 

amount  of  gelatin  chloride  formed  and  hence  the  value   of  z. 

Hence,  the  P.D.  should  increase  since  it  depends  on  log  (l  +  -j. 
We  also  increase  the  value  of  y,  but  z  and  y  will  not  increase  at 

the  same  rate,     z  can  be  calculated  from  the  equation  -  =  -  — 

y  x 

z  =  x2  -  y2  =  (x  +  y)(x  -  y) 

y  y 

When  little  acid  is  added  to  isoelectric  gelatin  the  value  of  z 
rises  more  rapidly  than  the  value  of  y,  while  when  more  acid  is 
added  the  reverse  happens.  This  is  obvious  from  Table  XIV 
comparing  the  variations  of  z  and  y  upon  the  addition  of  increas- 
ing quantities  of  HC1  to  isoelectric  gelatin. 

TABLE  XIV 


Cubic 

centimeters 

pHof 

0.1  N  acid 
in  100  c.c.  1 
per  cent 

gelatin 
solution 
at 

Cone,  y 
X105  N 

Cone,  z 

X10«  N 

z 
V 

*"<'+;) 

P.D.  cal- 
culated from 

29  log  (l+^-) 

P.D. 
observed, 
milli- 

originally 

equi- 

\       y  / 

millivolts 

volts 

isoelectric 

librium 

gelatin 

1.0 

4.56 

2.7 

16.5 

6.1 

0.8513 

24.7 

24.0 

2.0 

4.31 

4.9 

51.4 

10.5 

1.0607 

30.7 

32.0 

4.0 

4.03 

9.3 

132.5 

14.3 

1.  1847 

34.4 

33.0 

6.0 

3.85 

14.1 

200.0 

14.2 

1.  1818 

34.3 

32.5 

8.0 

3.33 

46.8 

343.0 

7.3 

0.9191 

26.1 

26.0 

10.0 

3.25 

56.2 

372.0 

6.6 

0.8808 

25.5 

24.5 

12.5 

2.85 

141.0 

477.0 

3.4 

0.  6435 

18.7 

16.5 

15.0 

2.52 

302.0 

608.0 

2.0 

0.4771 

13.8 

11.2 

20.0 

2.13 

741.0 

609.0 

0.82 

0.2601 

7.5 

6.4 

132  THEORY  OF  COLLOIDAL  BEHAVIOR 

The  fifth  vertical  column  of  the  table  shows  that  at  first  the 
value  -  increases  with  increasing  addition  of  acid  until  pH  =  4.03, 

\j 

and  that  with  the  addition  of  more  acid  the  value  -  diminishes 

again.     A  comparison  of  the  last  and  second  last  vertical  columns 
shows  that  the  observed  and  calculated  P.D.  agree. 

The  Donnan  equilibrium  thus  explains  mathematically  why 
the  P.D.  rises  at  first  when  HC1  is  added  to  isoelectric  gelatin 
until  the  pH  is  4.03,  and  why  the  P.D.  drops  when  the  pH  falls 
below  3.8.  No  other  colloidal  theory  is  able  to  explain  the 
curves  in  Fig.  41. 

THE  VALENCY  EFFECT 

Figure  41  shows  that  the  P.D.  curves  for  gelatin  chloride  and 
phosphate  are  considerably  higher  than  the  curve  for  gelatin 
sulphate.  The  same  valency  effect  was  observed  for  the  osmotic 
pressure  curves,  the  viscosity  curves,  and  the  curves  for  swelling. 
It  can  be  shown  that  the  Donnan  theory  demands  that  for  the 
same  pH  and  the  same  concentration  of  originally  isoelectric 
gelatin  the  P.D.  of  gelatin  chloride  and  gelatin  sulphate  should 
stand  in  the  exact  ratio  of  3 : 2,  and  it  is  one  of  the  most  convincing 
proofs  of  the  correctness  of  the  theory  that  the  calculated  values 
for  the  P.D.  of  these  two  gelatin  salts  agree  with  this  postulate. 
By  calculated  values  we  mean  the  value  59  (pH  inside  minus 
pH  outside). 

The  proof  that  the  values  for  pH  inside  minus  pH  outside  and, 
hence,  the  P.D.  of  the  solutions  of  the  two  gelatin  salts  must 
show  the  ratio  of  3 : 2  is  as  follows : 

The  equilibrium  equation  for  gelatin  chloride  is  of  the  second 
degree,  namely, 

x  _  y  +  z 
y~      x 
and  we  have  just  seen  that  by  proper  substitution  the 

P.  D.  =^  log  (  1-f  -)  millivolts. 
z          \         y/ 

The  equilibrium  equation  which  is  of  the  second  degree  when  the 
anion  is  monovalent  becomes  of  the  third  degree  when  the  anion 


MEMBRANE  POTENTIALS  133 

is  bivalent,  e.g.,  S04,  in  the  case  of  gelatin  sulphate.     Let  x  be  the 
concentration    of    hydrogen    ions    in    the    outside    solution,   y 

the  hydrogen  ion   concentration  in  the  inside  solution;  then  | 

is  the  concentration  of  the  SO4  ions  in  the  outside,  and  |  the 

concentration  of  the  SO4  ions  of  the  free  H2SO4  in  the   inside 
(gelatin)  solution.     The  concentration  of  SO4  ions  in  combination 

with  gelatin  becomes  ~-     Then  the  following  two   dissociation 
equations  must  hold : 

x2^  =  K  I  H2SO4J  undissociated    (outside) 

y2  (!  +  !)=  K[H2SO4]  undissociated    (inside) 

Since  the  undissociated  H2SO4  must  be  distributed  equally  on 
both  sides  of  the  membrane,  x3  =  y2(y  +  2);  x  =  [y2(y  -f  2)]*. 

x 
The  value  which  interests  us  is  -,  i.e.,  the  ratio  of  the  hydrogen  ion 

concentrations. 

Substituting  \yz(y  +  2)]*  for  x  in  -  we  get 


The  P.D.  is,  therefore,  in  the  case  of  gelatin  sulphate, 
P.D.  =  y  log  (l  +  p  millr 


millivolts 


while  in  the  case  of  gelatin  chloride  it  was 

CO  f  -V 

P.D.  =  7f  loglH--J  millivolts 
z          \        y/ 

Hence,  the  P.D.  of  gelatin  sulphate  solutions  should  be  only 
two-thirds  of  the  value  of  a  gelatin  chloride  solution  of  the 
same  pH  and  the  same  concentration  of  originally  isoelectric 
gelatin. 

This  theoretical  deduction  is  actually  fulfilled,  as  the  Tables 
XI,  XII,  and  XIII  show.  Thus  in  Table  XII  we  find  that  for 


134 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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gelatin  phosphate  of  pH  3.98  the 
calculated  P.D.  was  34.0  and  from 
Table  XIII  we  notice  that  for  gela- 
tin sulphate  of  pH  3.98  the  calcu- 
lated P.D.  was  22.2  millivolts.  This 
is  (within  the  limits  of  accuracy 
of  the  observations)  the  ratio  3:2, 
which  the  theory  demands.  For 
pH  4.31  the  P.D.  is  31  in  the  case 
of  gelatin  chloride  and  phosphate 
and  for  pH  4.34  it  was  20.5  for 
gelatin  sulphate,  again  the  ratio  of 
3:2.  The  strict  confirmation  of 
the  valency  ratio  came  out  clearly 
in  the  following  experiment  which 
was  undertaken  for  another  pur- 
pose— on  account  of  •  its  analogy 
with  antagonistic  salt  action — but 
which  shows  that  for  the  same  pH 
the  values  of  the  calculated  P.D. 
for  gelatin  chloride  and  sulphate 
are  in  the  ratio  of  3:2. 

Solutions  of  1  gm.  of  isoelectric 
gelatin  were  prepared  in  100  c.c.  of 
water  containing  5  c.c.  of  a  mixture 
of  0.1  N  HC1  and  0.1  N  H2SO4  in 
various  proportions.  The  solu- 
tions were  put  into  collodion  bags 
of  about  50  c.c.  volume  and  the  lat- 
ter were  put  into  350  c.c.  of  H2O 
containing  mixtures  of  N/1,000  HC1 
and  N/1,000  H2SO4  in  the  same 
proportions  as  inside.  The  arrange- 
ment was  that  described  for  os- 
motic pressure  measurements,  and 
the  osmotic  pressure,  P.D.,  and  pH 
inside  minus  pH  outside,  were 
measured  after  24  hours  at  24°C. 
The  upper  rows  of  Table  XV  give 


MEMBRANE  POTENTIALS  135 

the  ratio  of  cubic  centimeters  of  0.1  N  HC1  and  0.1  N  H2SO4 
in  100  c.c.  of  liquid.  The  rest  of  the  table  requires  no  further 
explanation.  As  in  all  gelatin-acid  salt  experiments,  the  agree- 
ment between  observed  and  calculated  P.D.  is  good. 

Both  P.D.  and  osmotic  pressure  are  depressed  the  more  the 
more  HC1  is  replaced  by  H2S04,  but  the  depressing  effect  is 
greater  in  the  case  of  osmotic  pressure  than  in  the  case  of  P.D. 
The  result  of  interest  to  us  is  the  following:  The  value  of  pH  inside 
minus  pH  outside  was,  for  gelatin  chloride  of  pH  3.64,  =  0.49,  and 
for  gelatin  sulphate  of  pH  3.64,  =  0.31.  The  ratio  of  the  two 
values  is  as  nearly  3:2  as  the  accuracy  of  the  measurements 
permits  us  to  expect.  The  values  for  the  observed  P.D.  agree 
with  the  values  of  the  calculated  P.D.  within  the  limits  of  ac- 
curacy of  the  measurements. 

This  quantitative  agreement  between  the  observed  P.D.  and 
the  P.D.  calculated  on  the  basis  of  the  Donnan  theory  leaves 
little  doubt  that  the  observed  P.D.  is  exclusively  determined  by 
the  Donnan  equilibrium. 

HYDROGEN  ION  AND  CHLORINE  ION  POTENTIALS 
If  we  write  the  equation  for  the  equilibrium  condition  between 
gelatin  chloride  solution  and  water  in  the  form 

y  _      x 
x      y  +z 

where  x  is  the  concentration  of  H  and  Cl  ions  in  the  outside 
solution,  y  the  concentration  of  the  H  and  Cl  ions  of  the  free  HC1 
inside  the  gelatin  chloride  solution,  and  z  the  concentration  of 

the  Cl  ions  in  combination  with  the  gelatin,  -  is  the  ratio  of 

x 

hydrogen  ion  concentration  inside  to  the  hydrogen  ion  concen- 

/>• 

tration  outside;  and  -        -  the  ratio  of  the  concentre 

y  -f  a 

chlorine  ion  outside  to  the  chlorine  ion  inside.     Since, 
and 


tration  outside;  and  — ^r—  the  ratio  of  the  concentration  of  the 
> 

log      =  pH  inside  minus  pH  outside 
x 


log  — j—  =  pCl  outside  minus  pCl  inside 

it  follows  that 

pH  inside  minus  pH  outside  =  pCl  outside  minus  pCl  inside  (2) 


136 


THEORY  OF  COLLOIDAL  BEHAVIOR 


If  Donnan's  membrane  equilibrium  is  the  cause  of  the  influence 
of  pH  on  the  P.D.  (and  on  the  other  physical  properties)  of 
protein  solutions,  we  must  be  able  to  show  that  equation  (2)  is 
actually  fulfilled. 

This  consequence  of  Donnan's  theory  was  put  to  a  test  and 
some  of  the  experiments  described  in  the  preceding  part  of  this 
chapter  were  selected  for  this  purpose.  Inside  the  collodion 
bags  were  1  per  cent  solutions  of  gelatin  chloride  of  different 
pH;  outside,  water.  After  18  hours  equilibrium  was  established 
between  inside  and  outside  solutions  and  the  pCl  as  well  as  the 
pH  was  ascertained.  The  pCl  was  determined  in  two  different 
ways  in  the  two  experiments;  in  one  experiment  it  was  deter- 
mined with  the  calomel  electrode,  in  the  other  it  was  determined 
in  the  gelatin  chloride  solution  by  titration  with  NaOH  according 
to  the  method  described  in  the  fourth  chapter.  Both  methods  of 
determining  the  pCl  led  to  the  result  that  the  value  pCl  outside 
minus  pCl  inside  was  for  the  same  solution  at  the  point  of  equilib- 
rium equal  to  the  value  pH  inside  minus  pH  outside  (within 
the  limits  of  accuracy  of  the  experiments) .  The  pCl  outside  was 
identical  with  the  pH  outside  since  the  outside  solution  contained 
only  free  HC1.  The  values  of  pH  were  all  determined  potentio- 
metrically  (Table  XVI). 

TABLE  XVI 
Experiment  1.     pCl  determined  by  titration 


pH  of  gelatin  chloride 

solution  at  equilibrium 

4.13 

3.69 

3.30 

3.10 

2.92 

2.78 

2.46 

2.26 

2.01 

1.76 

pH     inside     minus  pH 

outside  

0.56 

0.58 

0.50 

0.49 

0.44 

0.44 

0.33 

0.23 

0.15 

0.10 

pCl  outside  minus  pCl 

inside 

0  48 

0  51 

0  59 

0  44 

0  44 

0  38 

0  35 

0  22 

0  15 

0  11 

Experiment  2.     pCl  determined  electrometrically 


pH  of   gelatin   chloride 

solution  at  equilibrium 

4.04 

3.92 

3.78 

3.61 

3.46 

3.16 

2.73 

2.36 

2.04 

1.73 

pH    inside    minus    pH 

outside  

0.60 

0.62 

0.66 

0.55 

0.50 

0.43 

0.300.20 

0.12 

0.07 

pCl  outside  minus  pCl 

inside.  . 

0.55 

0.60 

0.57 

0.50 

0.53 

0.38 

0.32 

0.17 

0.12 

0.07 

MEMBRANE  POTENTIALS  137 

Nernst's  formula  leads  therefore  to  the  same  theoretical  P. D. 
regardless  of  whether  we  calculate  the  P.D.  on  the  basis  of 
the  difference  pH  inside  minus  pH  outside  or  on  the  basis  of 
the  difference  pCl  outside  minus  pCl  inside.  It  is  also  obvious 
that  both  assumptions  lead  to  the  same  sign  of  charge  of  the 
gelatin  chloride  solution.  If  we  assume  that  the  P.D.  is  deter- 
mined by  differences  in  the  hydrogen  ion  concentration,  the 
outside  solution  is  concentrated  and  the  inside  solution  dilute; 
if  the  P.D.  is  determined  by  differences  in  the  concentration  of 
the  Cl  ions,  the  inside  solution  is  concentrated  and  the  outside 
solution  dilute.  Since  the  common  ion  is  positive  in  the  former 
and  negative  in  the  latter  case,  the  gelatin  solution  becomes 
positive  in  both  cases. 

OUTSIDE  SOLUTION  INSIDE  SOLUTION 

H+   dilute  + 


—  H+   concentrated 

~,      ,.,    ,  membrane 

—  Cl-  dilute 


Cl~  concentrated 


The  facts  contained  in  this  section  of  this  chapter  prove  that 
the  equation  x2  =  y(y  +  z)  is  the  correct  expression  for  the 
Donnan  membrane  equilibrium  between  acid-salts  of  proteins 
with  monovalent  anion  and  water,  and  that  the  Donnan  equilib- 
rium accounts  for  the  P.D.  observed.  We  wish  to  point  out 
that  we  get  the  same  result  whether  we  determine  pCl  by  titra- 
tion  or  potentiometrically.  The  agreement  with  the  theory  is 
the  same  in  both  cases  though  the  accuracy  of  the  determination 
of  pCl  is  less  than  that  of  pH. 


THE  P.D.  OF  Na  GELATINATE 

The  Donnan  theory  demands  that  when  a  solution  of  Na 
gelatinate  contained  in  a  collodion  bag  is  in  equilibrium  with  a 
watery  solution  free  from  gelatin,  free  NaOH  should  be  forced 
from  the  inside  gelatin  solution  through  the  membrane  into  the 
outside  watery  solution  free  from  gelatin.  As  a  result  the  pH 
inside  will  now  be  less  than  pH  outside,  and  the  value  pH 
inside  minus  pH  outside  will  be  negative  for  Na  gelatinate  while 
it  was  positive  for  gelatin  chloride.  If  the  Donnan  equilibrium 
determines  the  P.D.  (as  it  does)  the  sign  of  charge  of  Na  gela- 
tinate must  be  the  reverse  from  what  it  was  for  gelatin  chloride. 


138 


THEORY  OF  COLLOIDAL  BEHAVIOR 


This  is  indeed  the  case  and  the 
turning  point  lies,  as  was  ex- 
pected, at  the  isoelectric  point. 

The  experiments  with  Na 
gelatinate  demand  more  rigid 
precautions  than  those  with 
gelatin  chloride.  It  is  neces- 
sary to  prevent  the  CO2  of 
the  air  from  diffusing  into 
the  alkaline  solutions  and 
therefore  the  outside  solution 
was  put  into  stoppered  bot- 
tles connected  with  the  outside 
air  by  glass  tubes  filled  with 
soda  lime.  On  account  of  the 
CO2  error  the  pH  measure- 
ments near  the  isoelectric  point 
are  unreliable  and  only  when 
the  pH  is  above  7.0  is  it  pos- 
sible to  get  reliable  results. 
The  main  facts  demanded  by 
the  theory  can,  however,  be 
demonstrated.  The  first  fact 
is  the  proof  that  the  sign  of 
charge  of  the  Na  gelatinate 
solution  is  the  reverse  of  that 
of  a  gelatin  chloride  solution. 

Collodion  bags  of  a  vol- 
ume of  about  50  c.c.  were 
filled  with  solutions  of  Na 
gelatinate  containing  1  gm. 
of  originally  isoelectric  gelatin 
and  varying  amounts  of  0.1  N 
NaOH  in  100  c.c.  solution. 
The  collodion  bags  were  dip- 
ped into  flasks  containing  500 
c.c.  of  aqueous  solutions  of 
NaOH  of  various  concentra- 
tions and  free  from  gelatin. 


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MEMBRANE  POTENTIALS  139 

The  flasks  were  sealed,  communicating  with  the  air  only  through 
tubes  filled  with  soda  lime,  as  stated.  The  collodion  bags  con- 
taining the  gelatin  were  closed  by  a  rubber  stopper  perforated 
by  a  glass  tube  which  served  as  a  manometer.  The  experiment 
lasted  6  hours  at  a  temperature  of  24° C.  The  results  of  the 
experiments  are  given  in  Table  XVII.  The  upper  horizontal 
row  gives  the  number  of  cubic  centimeters  of  0.1  N  NaOH 
originally  in  100  c.c.  of  the  gelatin  solution;  the  second  row 
gives  the  original  concentration  of  NaOH  in  the  outside  aqueous 
solution  free  from  gelatin ;  the  third  row  gives  the  osmotic  pressure 
in  mm.  H2O  after  6  hours.  The  next  row  gives  the  pH  inside 
and  the  following  row  the  pH  outside  after  the  experiment  was 
finished  (i.e.,  after  20  hours),  and  the  sixth  row  gives  the  differ- 
ence pH  inside  minus  pH  outside.  The  reader  will  notice  that 
this  difference  is  always  negative  with  one  exception,  which  is 
obviously  an  error.  The  last  two  rows  give  the  P.D.  calculated 
from  pH  inside  minus  pH  outside,  and  the  P.D.  observed. 

It  is  obvious  that  there  is  no  quantitative  agreement  between 
observed  and  calculated  P.D.  near  the  isoelectric  point.  As  soon 
as  the  pH  is  above  7.0  the  agreement  between  observed  and 
calculated  P.D.  becomes  better,  so  that  we  are  entitled  to  say 
that  the  difference  of  potential  between  a  Na  gelatinate  solution 
and  an  outside  solution  at  or  near  equilibrium  is  due  to  the 
Donnan  equilibrium  which  forces  the  expulsion  of  NaOH  from 
the  inside  into  the  outside  solution.  As  a  consequence  the  pH 
inside  becomes  lower  than  the  pH  outside. 


THE  INFLUENCE  OF  NEUTRAL  SALTS  ON  THE  P.D.  OF  GELATIN 
CHLORIDE  SOLUTIONS 

It  was  shown  in  Chapter  VI  that  the  addition  of  neutral  salts 
to  solutions  of  protein  salts  depresses  the  osmotic  pressure  or 
viscosity  of  these  solutions,  and  that  the  addition  of  neutral 
salts  to  a  gel  depresses  the  swelling  of  the  latter  (except  when  the 
solutions  and  gels  are  at  the  isoelectric  point).  It  was  of  interest 
to  find  out  whether  or  not  the  addition  of  a  salt  to  a  protein 
solution  depresses  also  the  P.D.  across  a  collodion  membrane, 
and  whether  this  is  also  due  to  a  depression  of  the  value  of  pH 


140  THEORY  OF  COLLOIDAL  BEHAVIOR 

inside  minus  pH  outside.  It  was  possible  to  show  that  this  is 
true. 

Gelatin  chloride  solutions  containing  1  gm.  of  originally  iso- 
electric  gelatin  in  100  c.c.  solution  and  having  a  pH  of  3.5  were 
made  up  in  different  concentrations  of  NaNO3  in  water,  the 
concentration  of  NaNO3  varying  from  M/4?096  to  M/32  NaNO3, 
and  all  possessing  a  pH  of  3.5.  These  mixtures  were  put  into  col- 
lodion bags  and  the  bags  were  put  into  HC1  solutions  of  pH  3.0 
made  up  in  different  concentrations  of  NaNO3,  also  of  pH  3.0. 
These  outside  solutions  contained  no  gelatin.  The  collodion  bags 
were  put  into  these  outside  solutions  free  from  gelatin  in  such  a 
way  that  the  concentration  of  the  NaNO3  solution  inside  the 
collodion  bag  was  always  the  same  as  outside. 

When  the  P.D.  across  the  collodion  membrane  was  measured 
after  18  hours  (after  equilibrium  was  established)  it  was  found 
that  it  was  diminished  upon  the  addition  of  neutral  salt  and  the 
more  the  higher  the  concentration  of  the  salt.  This  shows  that 
the  addition  of  neutral  salt  to  a  protein  solution  has  a  similar 
depressing  effect  on  the  P.D.  as  on  the  osmotic  pressure,  swelling, 
and  viscosity  of  the  protein  solutions. 

The  next  fact  of  interest  was  that  the  values  of  pH  inside 
minus  pH  outside  diminish  in  a  parallel  way  with  the  diminution 
of  the  P.D.  and  that  the  values  of  59  (pH  inside  minus  pH  outside) 
agree  remarkably  well  with  the  observed  P.D.  (Table  XVIII). 

We  have  seen  in  Chapter  VI  that  the  addition  of  a  salt  with 
bivalent  anion,  e.g.,  Na2SO4,  to  a  gelatin  chloride  solution  has  a 
much  greater  depressing  effect  on  the  osmotic  pressure,  viscosity, 
etc.,  of  the  solution  than  the  addition  of  a  salt  with  monovalent 
anion,  namely,  NaNO3.  It  can  be  shown  that  the  addition  of 
Na2SO4  also  has  a  greater  depressing  effect  on  the  P.D.  of  a 
gelatin  chloride  solution  than  has  a  NaNO3  solution  of  the  same 
molecular  concentration  (Table  XIX). 

We  will  consider  as  a  third  case  the  influence  of  CaCl2  on  the 
P.D.  of  a  gelatin  chloride  solution.  It  has  been  shown  that  the 
depressing  effect  of  CaCl2  on  the  osmotic  pressure  of  a  gelatin 
chloride  solution  is  about  twice  as  great  as  that  of  an  equimolec- 
ular  concentration  of  NaCl.  Table  XX  shows  that  the  depress- 
ing influence  of  CaCU  on  the  P.D.  is  about  twice  as  great  as 
that  of  NaNOs.  The  agreement  between  the  observed  P.D.  and 


MEMBRANE  POTENTIALS 


141 


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THEORY  OF  COLLOIDAL  BEHAVIOR 


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MEMBRANE  POTENTIALS  143 

the  value  59  (pH  inside  minus  pH  outside),  i.e.,  the  calculated 
P.D.,  is  excellent. 

It  is  of  importance  that  the  depressing  effect  of  salts  on  the  P.D. 
can  be  derived  from  the  Donnan  theory.  To  show  this  we  must 
remember  that  the  P.D.  is  expressed  by  the  following  term: 

P.D.  ==  Y  log  (l  +  -)  millivolts 

When  we  add  NaCl  to  a  gelatin  chloride  solution  we  increase  the 
concentration  of  the  chlorine  ions  not  in  combination  with  gela- 
tin, i.e.,  y,  while  the  concentration  z  of  the  Cl  ions  in  combination 
with  the  gelatin  remains  the  same,  provided  the  pH  remains  the 
same  (neglecting  the  diminution  of  ionization  of  gelatin  chloride). 
Hence,  the  P.D.  must  become  the  smaller  the  greater  y,  and  with 

steadily  increasing  y  and  constant  z  the  value  of  1  H —  must 

approach  1;  i.e.,  the  addition  of  enough  salt  must  depress  the 
P.D.  to  zero,  which  is  actually  the  case. 

This  is  also  true  when  we  add  another  salt,  e.g.,  NaNO3,  to  a 
gelatin  chloride  solution.  In  this  case  we  may  assume  that 
gelatin  nitrate  is  formed. 

The  depressing  effect  of  the  addition  of  NaCl  to  gelatin  chloride 
solution  on  the  P.D.  can  be  derived  from  the  values  of  pH 
inside  minus  pH  outside.  The  question  arises,  Why  is  it  correct 
to  neglect  the  influence  of  the  Na  ion?  The  writer  did  not  give 
any  reason  for  this  but  Dr.  J.  A.  Wilson  was  kind  enough  to  point 
out  in  a  letter  the  mathematical  proof  justifying  the  writer's 
procedure  in  the  following  way: 

"The  true  expression  of  the  P.D.  of  a  gelatin  chloride  solution 
the  presence  of  NaCl  is 

p  RT .      [HJ  outside  +  [NaJ  outside 

F     r  +1          r  +1 

LH  J  inside  +  |_NaJ  inside 

Let  the  system  contain  the  positive  ions  A,  B,  C,  etc.,  and  the 
negative  ions  M,  N,  0,  etc.,  whose  concentration  in  the  outside 
solution  are,  a,  b,  c,  m,  n,  o,  etc.,  and  in  the  inside  solution, 
a',  br,  etc.  From  the  published  work  of  Procter  and  Wilson  it  is 
evident  that  the  product  of  concentration  of  any  pair  of  op- 
positely charged  ions  is  equal  in  both  phases.  The  following 
equations  are  evident, 


144  THEORY  OF  COLLOIDAL  BEHAVIOR 

a  X  m  =  a'  X  in' 
b  x  m  =  b'  X  m' 

(a  +  b  +  c  +  .    .    .    )m  =  (a'  +  6'  +  c'  +  .    .    .   X 
(a  +  6  +  c  +  .    .    )(w  +  n  +  o  +  .    .    .    )  = 

(a'  +  6'  +  c'   +      ...    )(ro'  +  n'  +  o'  +  .    .     .   ) 
whence 

a         b    _c         a  +  6  +  c  +  .    .    .  " 
a7  ==  6'  ~?  ==  a'  +  6'  +  c'  +  .    .    . 

It  is,  therefore,  immaterial  which  ion  is  singled  out  for  the 
calculation  of  the  P.D.  on  the  basis  of  the  Donnan  effect.  For 
the  sake  of  the  accuracy  of  measurement  the  hydrogen  ion  was 
selected. 

It  is  perhaps  worth  while  to  point  out  that  the  agreement 
between  calculated  and  observed  P.D.  is  better  in  the  experi- 
ments with  salts  than  in  the  experiments  without  salts,  especially 
near  the  isoelectric  point.  It  seems  almost  as  if  the  presence  of 
too  low  a  concentration  of  electrolyte  increased  the  error  of  the 
measurements . 


THE  INFLUENCE  OF  THE  SIGN  OF  CHARGE 

The  fact  that  the  P.D.  of  a  protein-acid  salt  solution  is   a 

function  of  the  term  log  (1  +  -),  where  z  is  the  concentration  of 

y 

the  anion  in  combination  with  the  protein  ions  and  y  the  con- 
centration of  the  anion  of  the  free  acid,  explains  a  phenomenon 
which  is  fundamental  in  colloidal  behavior,  namely,  that  when- 
ever a  salt  depresses  any  physical  property  of  a  protein  (or  a 
colloidal  solution  in  general)  this  action  is  due  to  that  ion  of  the 
salt  which  has  the  opposite  sign  of  charge  to  that  of  the  protein 
ion.  That  this  is  true  for  the  influence  of  salts  on  viscosity, 
osmotic  pressure,  and  swelling  has  been  discussed  in  Chap.  VI, 
and  we  shall  see  that  it  is  true  also  for  the  precipitation  of  certain 
protein  solutions.  In  the  latter  case  it  is  known  as  Hardy's  rule 
of  the  precipitating  action  of  salt.  In  all  these  cases  the  effi- 
ciency of  the  salt  increases  with  the  valency  of  the  efficient 
ion  of  the  salt.  These  rules  are  a  consequence  of  the  Donnan 


MEMBRANE  POTENTIALS  145 

equilibrium.     The  term  derived  from  the  equilibrium  equation, 
log  (1  -\ — )  makes  the  P.D.  a  function  of  z  and  y,  i.e.,  that  ion 
which  has  the  opposite  sign  of  charge  to  the  protein  ion. 
THE  INFLUENCE  OF  THE  CONCENTRATION  OF  PROTEIN  ON  THE  P.D. 

While  the  addition  of  neutral  salt  depresses  the  P.D.  of  protein 
solutions  across  a  membrane  (as  it  depresses  all  the  other  prop- 
erties) the  addition  of  protein  has  the  opposite  effect,  increasing 
the  P.D.  (as  it  increases  also  the  other  properties).  This  influ- 
ence of  the  concentration  of  the  protein  follows  mathematically 

from  the  equilibrium  equation.     Since  P.D.  =  -=-  log  (1  +  -) 

*  y 

millivolts,  it  is  obvious  that  if  y  remains  constant  (i.e.,  if  no  salt 
is  present  and  the  pH  remains  the  same)  while  z  increases  as  a 
consequence  of  the  increase  of  the  concentration  of  protein,  the 
P.D.  must  rise  with  the  concentration,  and  this  was  found  to  be 
the  case. 

Collodion  bags,  connected  with  glass  manometers  in  the  way 
described,  containing  50  c.c.  of  different  concentrations  of  origi- 
nally isoelectric  gelatin  varying  from  0.125  per  cent  to  2  per  cent 
and  containing  enough  H3PO4  to  bring  the  gelatin  solution  to  a 
pH  of  3.5  were  put  into  beakers  containing  350  c.c.  H3PO4 
solution  of  pH  3.5.  In  order  to  prevent  dilution  of  the  protein 
solution  through  osmosis,  the  glass  manometers  were  filled  at 
the  beginning  of  the  experiment  with  the  same  gelatin  phosphate 
solution  as  that  contained  in  the  collodion  bag,  to  that  height 
which  the  osmotic  pressure  measured  in  preceding  experiments 
amounted  to.  After  about  20  hours  the  pH  in  the  inside  and  the 
outside  solutions  and  the  P.D.  across  the  membrane  were  meas- 
sured.  Some  of  the  experiments  were  made  in  duplicate  (Table 
XXI). 

It  is  obvious,  first,  that  the  P.D.  increases  with  the  concentra- 
tion of  gelatin,  and  second,  that  the  increase  of  P.D.  observed 
agrees  quantitatively  with  the  increase  calculated  on  the  assump- 
tion of  the  validity  of  Donnan's  theory. 

THE  P.D.  OF  SOLUTIONS  OF  CRYSTALLINE  EGG  ALBUMIN 

The  experiments  mentioned  thus  far  had  all  been  done  on 

gelatin.     It  was  of  importance  to  determine  whether  or  not 
10 


146 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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MEMBRANE  POTENTIALS  147 

these  results  could  be  confirmed  with  crystalline  egg  albumin. 
This  was  found  to  be  the  case,  and  the  experiments  on  the 
membrane  potentials  of  the  solutions  of  the  chloride  of  crystalline 
egg  albumin  showed  a  perfect  quantitative  agreement  with  the 
theory. 

Collodion  bags  of  about  50  c.c.  volume  were  filled  with  a  solu- 
tion of  1  per  cent  crystalline  egg  albumin  containing  varying 
amounts  of  0.1  N  HC1,  and  the  bags  were  put,  as  usual,  into 
beakers  containing  350  c.c.  of  HC1  solutions  of  different  concen- 
tration but  free  from  albumin.  The  first  two  horizontal  rows 
of  Table  XXII  give  the  amount  of  0.1  N  HC1  in  each  solution. 
The  experiments  were  carried  out  at  a  temperature  of  24°C., 
and  after  22  hours  the  osmotic  pressure,  P.D.,  and  pH  of  inside 
(albumin)  solution  and  pH  of  the  outside  solution  were  measured. 
The  albumin  used  was  not  isoelectric,  but  since  it  had  been 
prepared  after  S0rensen's  method  it  was  probably  partly  am- 
monium albuminate,  with  a  pH  of  near  6.0.  The  table  shows  that 
the  calculated  and  observed  P.D.  agree  beautifully  (especially  on 
the  acid  side  of  the  isoelectric  point) ;  that  the  P.D.  is  a  minimum 
near  pH  4.70  of  the  albumin  (i.e.,  near  the  isoelectric  point,  which 
is  at  pH  4.8),  and  that  the  albumin  is  positively  charged  on  the 
acid  and  negatively  charged  on  the  alkaline  side  of  the  isoelectric 
point.  This  is  again  in  harmony  with  what  we  should  expect 
on  the  basis  of  the  Donnan  equilibrium. 

The  next  problem  was  to  determine  the  influence  of  the  addi- 
tion of  a  neutral  salt  to  a  solution  of  the  chloride  of  crystalline 
egg  albumin.  A  1  per  cent  solution  of  crystalline  egg  albumin 
containing  7  c.c.  of  0.1  N  HC1  in  100  c.c.  was  made  up  in  various 
concentrations  of  NaCl.  The  collodion  bags  containing  these 
albumin  chloride-NaCl  mixtures  were  dipped  into  beakers  con- 
taining 350  c.c.  of  the  same  concentration  of  NaCl  as  that  of  the 
albumin  solution,  and  all  made  up  in  N/1,000  HC1.  The  experi- 
ment was  carried  out  at  24°C.  and  the  measurements  were  made 
after  22  hours. 

Table  XXIII  gives  the  results,  which  show  again  a  beautiful 
agreement  between  calculated  and  observed  P.D. 

We  may,  therefore,  conclude  that  the  P.D.  of  both  gelatin 
solutions  and  solutions  of  crystalline  egg  albumin  separated  by  a 
collodion  membrane  from  a  watery  solution  free  from  protein  is 


148 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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MEMBRANE  POTENTIALS  149 

exclusively  determined  by  the  Donnan  equilibrium,  since 
otherwise  the  quantitative  agreement  between  the  observed 
P.D.  and  the  values  calculated  from  Donnan's  equation  would 
be  impossible. 

It  may  be  stated,  finally,  that  since  P.D.  =  29  log  (l  +  |) 

millivolts,  it  follows  that  the  addition  of  a  non-electrolyte  to  a 
gelatin  chloride  solution  cannot  influence  the  P.D.  since  the 

addition  of  a  non-electrolyte  cannot  affect  the  value  of  -• 

The  expression  for  P.D.  also  explains  why  the  P.D.  is  zero 
at  the  isoelectric  point  of  a  protein,  since  z  becomes  zero  at  that 
point.  Moreover,  it  is  obvious  that  the  addition  of  a  neutral 
salt  to  a  solution  of  isoelectric  gelatin  cannot  further  depress 
the  P.D.  or  cause  a  reversal  in  the  sign  of  the  charge. 

Donnan's  theory  of  membrane  equilibrium  therefore  explains 
mathematically  and  quantitatively  the  P.D.  observed  at  equi- 
librium between  a  protein  solution  and  a  watery  solution  free 
from  protein,  separated  by  a  membrane.  It  does  not  happen 
very  often  that  every  postulate  of  a  theory  is  fulfilled  by  the 
observation  as  it  is  in  this  case. 

The  bearing  of  this  fact  upon  the  theories  of  colloidal  behavior 
is  as  follows:  The  P.D.  is  influenced  by  the  hydrogen  ion  con- 
centration, by  the  valency  of  the  ion,  by  the  addition  of  neutral 
salt  in  the  same  way  as  are  the  other  properties  of  protein,  such 
as  osmotic  pressure,  viscosity,  and  swelling.  Since  the  Donnan 
theory  explains  this  influence  of  pH,  valency,  and  salt  effect  on 
P.D.  with  mathematical  accuracy,  it  seems  at  least  highly 
probable  that  it  may  also  explain  the  other  colloidal  properties 
of  proteins  in  the  same  way,  with  this  difference  only,  that  the 
experimental  error  is  much  greater  in  the  measurements  of  the 
other  properties  than  in  the  measurements  of  P.D. 


CHAPTER  IX 

THE  ORIGIN  OF  THE  ELECTRICAL  CHARGES  OF  MICEL- 
LAE, AND  OF  LIVING  CELLS  AND  TISSUES 

1.  STABILITY  or  SUSPENSIONS,  ELECTRICAL  CHARGES  OF 
MICELLAE,   AND  DONNAN  EQUILIBRIUM 

The  stability  of  suspensions  is,  perhaps,  the  chief  problem  of  a 
theory  of  colloidal  behavior.  Hardy1  has  shown  that  this  prob- 
lem is  linked  with  the  problem  of  the  origin  of  the  electrical 
charges  of  the  particles  in  suspension,  since  such  particles  are 
forced  by  mutual  electrostatic  repulsion  to  remain  in  suspension. 
By  his  experiments  on  the  migration  of  suspended  particles  of 
coagulated  white  of  egg  in  an  electrical  field  he  proved  that  they 
have  a  positive  charge  in  the  presence  of  acid,  a  negative  charge 
in  the  presence  of  alkali,  and  no  charge  at  an  intermediate  point 
which  he  termed  the  isoelectric  point  of  the  particles.  He  was 
able  to  demonstrate  that  the  stability  of  colloidal  suspensions  is 
a  minimum  at  the  isoelectric  point. 

He  and  others  found,  moreover,  that  low  concentrations  of 
neutral  salts  diminish  the  stability  of  colloidal  suspensions  in 
the  presence  of  acids  or  alkalies  and  that  the  efficient  ion  of  the 
salt  has  the  opposite  sign  of  charge  to  that  of  the  colloidal 
particle,  since  the  precipitating  efficiency  of  a  salt  increases 
rapidly  with  the  valency  of  that  ion  of  the  salt  which  has  the 
opposite  sign  of  charge  to  that  of  the  colloidal  particles.  It 
seemed  natural  to  infer  that  the  precipitation  of  colloidal  sus- 
pensions by  low  concentrations  of  a  salt  was  caused  by  an 
annihilation  of  the  charge  of  the  colloidal  particle.  The  problem 
of  the  stability  of  the  colloidal  suspension  then  developed  into 
the  problem  of  accounting  for  this  peculiar  behavior  of  the 
electrical  charges  of  colloidal  particles. 

Hardy's  original  idea  was  that  the  H  ions  of  the  acid  or  OH 

1  HARDY,  W.  B.,  Proc.  Roy.  Soc.,  vol.  66,  p.  110,  1900. 

150 


THE  ELECTRICAL  CHARGES  OF  MICELLA  151 

ions  of  the  alkali  were  adsorbed  by  the  colloidal  particle  in  pref- 
erence to  the  other  ions  on  account  of  their  greater  rapidity  of 
migration;1  and  this  idea  was  also  accepted  by  Perrin2  in  his 
experiments  on  electrical  endosmose,  where  it  was  necessary 
to  account  for  the  fact  that  certain  membranes  become  posi- 
tively charged  in  the  presence  of  acid  and  negatively  in  the 
presence  of  alkali.  Those  who  accept  the  adsorption  hypothesis 
explain  the  fact  that  the  electrical  charges  of  the  particles  are 
apparently  diminished  or  destroyed  by  the  addition  of  a  salt  on 
the  assumption  of  a  preferential  adsorption  of  one  of  the  ions  of 
the  salt  by  the  micellae;  yet  such  an  assumption  is  incompatible 
with  the  purely  stoichiometrical  behavior  of  proteins.  It  is 
also  difficult  to  account  on  the  basis  of  the  adsorption  hypothesis 
for  the  fact  that  the  addition  of  little  acid  increases  while  the 
addition  of  more  acid  depresses  the  electrical  charge  of  micellae. 

A  second  possibility  was  pointed  out  by  the  writer  in  1904, 3 
namely,  that  Hardy's  migration  experiments  might  be  explained 
in  the  case  of  proteins  by  the  fact  that  proteins  are  amphoteric 
electrolytes  which  in  the  presence  of  alkali  dissociate  electro- 
lytically  by  giving  rise  to  a  protein  anion  and  in  the  presence  of 
acid  giving  rise  to  a  protein  cation;  while  at  the  isoelectric  point 
no  protein  ion  would  be  formed.  This  idea  could,  however,  not 
explain  why  the  addition  of  a  salt  in  low  concentration  should 
diminish  the  charge  of  aggregates  of  ions,  i.e.,  the  micellae,  except 
by  assuming  that  in  this  case  the  electrolytic  dissociation  of  the 
protein  salts  should  be  repressed.  The  concentration  of  salts 
required  for  the  precipitation  of  colloidal  suspensions  is,  however, 
much  too  small  to  make  such  a  suggestion  acceptable.  The 
idea  is,  however,  correct  if  applied  to  the  migration  of  isolated 
protein  ions  in  the  electrical  field. 

In  1916  J.  A.  Wilson4  suggested  that  these  electrical  charges  of 
micellae  were  caused  by  the  establishment  of  a  Donnan  equilib- 
rium between  the  colloidal  particle  and  the  surrounding  solution. 
There  were,  however,  no  measurements  of  membrane  potentials 

1  HARDY,  W.  B.,  J.  physiol,  vol.  29,  p.  xxvi,  1903. 

2  PERRIN,  J.,  J.  chim.  physique,  vol.  2,  p.  601,  1904;  vol.  3,  p.  50,  1905. 
Notice  sur  les  titres  et  travaux  scientifiques  de  M.  JEAN  PERRIN,  Paris, 
1918. 

3  LOEB,  J.,  Univ.  Cat.  Pub.,  Physiology,  vol.  1,  p.  149,  1904. 

4  WILSON,  J.  A.,  J.  Am.  Chem.  Soc.,  vol.  38,  p.  1982,  1916. 


152  THEORY  OF  COLLOIDAL  BEHAVIOR 

available  at  that  time  and  this  was  probably  the  reason  that  his 
suggestion  was  not  accepted. 

We  may  consider  a  protein  solution  inside  a  collodion  bag  and 
surrounded  by  a  watery  solution  as  a  model  of  a  protein  micella 
suspended  in  a  watery  solution.  In  that  case  it  can  be  shown 
that  the  electrical  charge  of  such  a  model  varies  in  exactly  the 
same  way  as  the  charges  of  colloidal  particles  in  suspension, 
e.g.,  coagulated  egg  albumin. 

1.  The  electrical  charge  of  the  micella  model  (i.e.,  gelatin  solu- 
tion in  a  collodion  bag)  is  zero  at  the  isoelectric  point. 

2.  The  charge  of  the  model  is  positive  on  the  acid  side  and 
negative  on  the  alkaline  side  of  the  isoelectric  point  of  gelatin  and 
of  crystalline  egg  albumin. 

3.  The  charge  of  the  model  increases  with  the  addition  of  little 
acid  and  diminishes  with  the  addition  of  more  acid  to  isoelectric 
particles. 

4.  The  charge  of  the  model  is  diminished  by  the  addition  of  low 
concentrations  of  neutral  salts,  and  the  depressing  action  of  the 
salt  increases  rapidly  with  the  valency  of  that  ion  of  the  neutral 
salt  which  has  the  opposite  sign  of  charge  to  that  of  the  micella. 

It  has  been  shown  in  the  preceding  chapter  that  these  facts 
can  be  explained  not  only  qualitatively  but  quantitatively  from 
the  theory  of  Donnan's  membrane  equilibrium.  This  quantita- 
tive agreement  leaves  no  doubt  that  the  electrical  charge  of  this 
micella  model  is  caused  exclusively  by  the  Donnan  equilibrium. 

2.  THE    ELECTRICAL    CHARGE    OF    SUSPENDED    PARTICLES    OF 
POWDERED  GELATIN 

We  may  ask  whether  it  is  justifiable  to  consider  a  gelatin  solu- 
tion enclosed  in  a  collodion  bag  and  surrounded  by  an  aqueous 
solution  as  a  model  of  a  micella.  This  is  theoretically  correct 
since  the  colloidal  behavior  of  both  a  true  micella  as  well  as  the 
protein  solution  in  a  collodion  bag  is  due  to  the  same  condition, 
namely,  that  the  protein  ion  is  prevented  from  diffusing  into  the 
outside  aqueous  solution  while  no  such  block  exists  for  the  diffu- 
sion of  the  crystalloidal  ions.  The  block  which  prevents  the 
diffusion  of  the  protein  ions  in  the  model  is  the  collodion  mem- 
brane, while  in  the  case  of  the  micella  (or  a  solid  jelly)  it  is  the 


THE  ELECTRICAL  CHARGES  OF  MICELLA  153 

cohesion  between  the  protein  ions  themselves.  The  formation  of 
a  micella  depends  upon  these  cohesive  forces  between  the  protein 
ions  (or  parts  of  these  ions)  becoming  stronger  than  the  attractive 
forces  between  the  protein  molecules  and  the  molecules  of  water. 
The  nondiffusibility  of  the  protein  ions  of  the  micella  must  give 
rise  to  the  establishment  of  a  Donnan  equilibrium  between  the 
micella  and  the  surrounding  liquid,  and  this  equilibrium  must 
give  rise  to  the  electrical  charge  of  the  micella.  The  only  ques- 
tion is  how  far  the  agreement  between  Donnan's  theory  and  the 
observed  charge  goes  in  the  case  of  true  micellae.  To  test  this  we 
used  suspensions  of  particles  of  powdered  gelatin  in  water.  If  it 
can  be  shown,  first,  that  these  particles  assume  electrical  charges 
when  suspended  in  water,  second,  that  these  charges  vary  in  the 
usual  way  with  pH  and  the  presence  of  salts,  and  third,  that  these 
charges  can  be  derived  from  the  Donnan  equilibrium,  the  theory 
of  these  charges  as  well  as  the  theory  of  the  stability  of  colloidal 
suspensions  can  be  put  on  an  exact  scientific  basis. 

The  method  of  these  experiments  was  as  follows:  Powdered 
particles  of  isoelectric  gelatin  were  put  into  a  solution  of  acid  or 
alkali  at  a  temperature  of  20°C.  and  allowed  to  remain  there  for  a 
number  of  hours  to  allow  a  complete  or  approximate  equilibrium 
to  be  established  between  the  inside  of  the  micellae  and  the  outside 
solution.1  The  temperature  must  not  be  above  20°,  since  other- 
wise the  granules  of  gelatin  will  dissolve  too  rapidly.  After  a 
number  of  hours  the  suspended  particles  were  separated  from 
the  outside  solution  by  filtration,  the  gelatin  was  melted  and  put 
into  vessels  with  two  bent  tubes  (see  Fig.  42).  After  the  gelatin 
had  set  to  a  gel  (by  cooling)  the  P.D.  between  the  solid  gel  and 
the  outside  solution  (filtrate)  was  determined  with  the  electro- 
meter. The  P.D.  was  that  of  the  following  cell: 


calomel 
electrode 


saturated 
KC1 


outside 
watery 
solution 


solid  gel 


saturated 
KC1 


calomel 
electrode 


Everything  else  being  symmetrical  the  P.D.  measured  was  that 
between  the  suspended  particles  of  gelatin  (solid  gel)  and  the 
outside  solution  with  which  the  gelatin  micellae  had  been  in 
complete  or  approximate  equilibrium. 

1  LOEB,  J.,  J.  Gen.  Physiol,  vol.  4,  p.  351,  1921-22. 


154 


THEORY  OF  COLLOIDAL  BEHAVIOR 


It  can  be  shown  that  the  P.D.  between  the  micellae  and  the 
surrounding  solution  is  influenced  in  the  same  way  by  pH, 
valency,  and  salts  as  is  the  P.D.  between  a  protein  solution  and  a 
watery  solution  separated  from  each  other  by  a  collodion  mem- 
brane. It  was  then  necessary  to  ascertain  whether  this  P.D. 
was  due  to  Donnan  equilibrium,  and  for  this  purpose  the  pH 


Fia.  42. — Method  of  measuring  P.D.  between  gel  and  surrounding  solution. 


inside  of  the  (melted)  gelatin  micellae  and  the  pH  of  the  outside 
solution  were  measured  with  the  hydrogen  electrode  and  the 
potentiometer.  It  was  found  that  the  value  58  (pH  inside  the 
micellae  minus  pH  outside)  agreed  as  closely  with  the  P.D. 
observed  with  the  Compton  electrometer  as  the  accuracy  of  the 
measurements  permitted.  This  makes  it  highly  probable  that 
the  electrical  charge  of  the  micellae  is  determined  by  the  Donnan 
equilibrium.  We  will  again  call  the  value  58  (pH  inside  micellae 
minus  pH  outside)  the  calculated  P.D.  though  it  was  in  reality 
also  observed.  The  accuracy  of  the  P.D.  measurements  is  not  as 
great  as  in  the  case  of  the  experiments  of  the  preceding  chapter, 
for  reasons  which  we  have  not  yet  been  able  to  ascertain. 


THE  ELECTRICAL  CHARGES  OF  MICELLAE  155 

3.  THE    INFLUENCE   OF   pH   ON   THE  CHARGE   OF  SUSPENDED 

PARTICLES  OF  POWDERED  GELATIN 

One-gram  samples  of  powdered  isoelectric  gelatin  going  through 
mesh  30  but  not  through  mesh  60  were  put  into  350  c.c.  of  water 
containing  various  quantities  of  HC1  (see  first  horizontal  row  of 
Table  XXIV),  and  left  in  these  solutions  for  24  hours  at  20°C. 
The  mixtures  were  occasionally  stirred.  After  24  hours  the 
relative  volume  of  the  particles  was  measured  and  they  were  put 
on  a  filter  to  allow  the  acid  to  drain  off.  The  gelatin  was  then 
melted  by  heating  to  45°C.  and  poured  into  glass  cylinders  which 
at  their  lower  end  had  two  glass  side  tubes  attached  (Fig.  42). 
The  mass  was  then  allowed  to  solidify  by  cooling  and  the  P.D. 
between  gelatin  and  watery  solution  was  ascertained.  One  of  the 
two  glass  tubes  dipped  into  a  beaker  containing  the  outside  HC1 
solution  (the  filtrate)  with  which  the  gelatin  had  been  in  equilib- 
rium, and  the  other  dipped  into  a  beaker  containing  a  saturated 
solution  of  KC1.  Each  beaker  was  connected  with  a  calomel 
electrode  (filled  with  saturated  KC1)  leading  to  a  Compton 
electrometer.  The  last  row  in  Table  XXIV  gives  the  observed 
P.D.  in  millivolts. 

The  pH  of  the  melted  gelatin  was  determined  potentiometri- 
cally.  This  is  called  pH  inside  in  Table  XXIV.  The  pH  of  the 
outside  solutions  (filtrate)  was  also  determined. 

While  the  agreement  between  the  observed  P.D.  and  the  value 
of  59  (pH  inside  micellae  minus  pH  outside)  is  not  as  good  as  in  the 
experiments  with  collodion  bags,  it  is  at  least  sufficient  to  leave 
no  doubt  that  the  charge  is  caused  by  the  Donnan  equilibrium  in 
the  way  discussed  in  the  preceding  chapter. 

4.  THE  INFLUENCE  OF  ACID  AND  ALKALI  ON  THE  SIGN  OF  CHARGE 

OF  MICELLAE 

In  Hardy's  experiment  with  white  of  egg  the  particles  were 
positively  charged  on  the  acid  side  of  the  isoelectric  point  and 
negatively  charged  on  the  alkaline  side.  It  can  be  shown  that 
this  is  also  true  for  the  charges  of  the  suspended  particles  of 
powdered  gelatin,  and  that  this  change  of  sign  of  charge  of  these 
particles  by  going  from  the  acid  to  the  alkaline  side  of  the  iso- 


156 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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THE  ELECTRICAL  CHARGES  OF  MICELLA  157 

electric  point  is  accompanied  by  a  change  in  the  sign  of  the  value 
(pH  inside  micellae  minus  pH  outside). 

One  gram  of  powdered  gelatin  of  grain  size  between  mesh  30 
and  60,  rendered  isoelectric,  was  put  into  each  of  a  series  of 
closed  flasks  containing  350  c.c.  of  distilled  water  with  varying 
quantities  of  0.1  N  HC1  or  NaOH  per  100  c.c.  (see  Table  XXV). 
The  temperature  was  20°C.  After  4  hours  the  powdered  gelatin 
was  separated  from  its  supernatant  liquid  by  filtration,  the  gela- 
tin was  melted  and  the  pH  of  the  melted  gelatin  and  of  the  outside 
solution  (filtrate)  were  measured.  The  gelatin  was  then  solidi- 
fied and  the  P.D.  between  the  solid  gelatin  and  the  filtrate  (out- 
side solution)  determined,  as  described.  The  results  of  the 
experiments  are  given  in  Table  XXV.  The  first  row  gives  the 
number  of  cubic  centimeters  of  0.1  N  HC1  or  NaOH  contained 
originally  in  100  c.c.  outside  solution.  The  next  row  gives  the 
relative  volume  of  the  solid  mass  of  gelatin,  i.e.,  the  degree  of 
swelling.  The  rest  of  the  table  needs  no  explanation.  It  is 
obvious  that  pH  inside  minus  pH  outside  is  positive  as  long  as  the 
pH  of  the  gelatin  is  on  the  acid  side  of  the  isoelectric  point,  while 
it  is  negative  when  the  gelatin  is  on  the  alkaline  side  of  the  iso- 
electric point.  The  turning  point  is  approximately  at  the  iso- 
electric point,  but  the  measurements  near  the  isoelectric  point 
are  obviously  vitiated  by  experimental  errors  and  possibly  by 
some  other  factor,  so  that  we  cannot  demonstrate  more  by  the 
experiment  than  that  suspended  particles  of  solid  metal  gelatinate 
have  the  opposite  sign  of  charge  to  that  of  the  micellae  of  gelatin 
chloride,  and  that  this  difference  is  accompanied  by  a  reversal  of 
the  sign  of  the  value  of  pH  inside  minus  pH  outside,  which  is 
positive  in  the  case  of  gelatin  chloride  and  negative  in  the  case 
of  Na  gelatinate.  It  may  also  be  pointed  out  that  the  minimum 
of  swelling  (volume)  coincides  with  the  minimum  of  P.D. 

5.  THE  INFLUENCE  OF  SALTS  ON  THE  CHARGE  OF  SUSPENDED 
PARTICLES  OF  GELATIN 

The  most  important  fact  which  a  theory  of  the  electrical  charge 
of  colloidal  micellse  is  expected  to  explain  is  the  annihilation  of 
these  charges  by  neutral  salts.  Those  who  believe  in  the  adsorp- 
tion theory  assume  that  both  ions  of  a  neutral  salt  are  adsorbed 


158  THEORY  OF  COLLOIDAL  BEHAVIOR 

by  the  colloidal  particles,  and  that  the  salt  ion  with  the  opposite 
sign  of  charge  to  that  of  the  colloidal  particle  diminishes  the 
charge  of  the  latter,  while  the  salt  ion  with  the  same  sign  of  charge 
as  the  colloidal  particle  increases  the  charge  of  the  latter,  and  the 
more  the  higher  the  valency  of  the  ion  of  the  salt.  The  idea  that 
such  an  adsorption  occurs  is  definitely  refuted  by  the  experiments 
discussed  in  Chap.  II  (see  Figs.  1  and  2).  It  might,  however, 
be  possible  that  the  ion  with  the  same  sign  of  charge  as  the 
colloidal  particle  might  increase  the  charge  of  the  colloidal 
particle  in  some  other  way  than  through  adsorption,  and  it  was 
necessary  to  test  this  possibility,  which  has  found  acceptance  on 
the  part  of  some  chemists.  The  writer's  experiments  on  anomal- 
ous osmosis  have  shown  that  when  a  dilute  solution  of  a  salt  is 
separated  from  pure  water  by  a  collodion  membrane  coated 
with  gelatin,  if  the  salt  solution  and  the  water  are  brought  to  the 
same  pH  by  adding  an  acid,  e.g.,  HNO3,  the  potential  difference 
on  the  two  opposite  sides  of  the  membrane  increases  with  the 
valency  of  the  cation  of  the  salt  used,  i.e.,  in  the  order 

Ce>Ca>Na 

This  influence  was  found  to  be  due  to  a  diffusion  potential.1 
Nevertheless  it  seemed  necessary  to  determine  whether  or  not 
these  cations  influenced  the  charge  of  suspended  particles  of 
gelatin  chloride  in  the  same  way.  If  this  were  true,  the  depress- 
ing effect  of  CeCl3  on  the  charge  of  the  micellae  should  be  less 
than  the  depressing  effect  of  CaCl2,  and  the  depressing  effect  of 
CaCl2  should  be  less  than  the  depressing  effect  of  Nad,  provided 
the  pH  is  on  the  acid  side  of  the  isoelectric  point. 

If,  on  the  other  hand,  the  Donnan  effect  alone  determines  the 
depressing  effect  of  the  salt  on  the  charge  of  the  suspended 
particles  of  gelatin,  this  depressing  effect  should  be  exclusively 
due  to  the  anion  of  the  salt  on  the  acid  side  of  the  isoelectric 
point  of  the  gelatin,  while  the  cation  of  the  salt  should  have  no 
effect.  This  follows  from  the  discussion  in  the  preceding  chapter 
according  to  which  the  P.D.  between  gelatin  chloride  solution 

and  water  is  determined  by  the  value  of  log  (1  +  -),  where  z 

y 
and  y  are  the  anions.     The  cations  do  not  enter  into  the  term  on 

1  LOEB,  J.,  J.  Gen.  Physiol.,  vol.  4,  pp.  213,  463,  1921-22. 


THE  ELECTRICAL  CHARGES  OF  MICELLA  159 

the  acid  side  of  the  isoelectric  point.  We  shall  see  that  the  meas- 
urements of  the  P.D.  between  micellae  and  surrounding  solution 
are  sufficiently  accurate  to  leave  no  doubt  that  the  Donnan  equi- 
librium alone  determines  the  charge  of  the  micellae  and  that  the 
cation  of  the  salt  does  not  increase  the  charge  of  the  micellae  of 
gelatin  chloride. 

In  order  to  get  accurate  measurements  it  was  necessary  to  use 
micellae  of  gelatin  chloride  of  a  pH  sufficiently  far  from  the  iso- 
electric point  to  avoid  the  errors  of  the  measurements  which 
occur  near  that  point.  We  weighed  out  doses  of  1  gm.  of 
powdered  gelatin  of  a  pH  of  near  7.0  and  made  them  isoelectric  by 
treatment  with  M/128  acetic  acid  and  subsequent  washing  as 
described  in  Chap.  II.  In  this  process  some  gelatin  was  dis- 
solved and  lost  (probably  about  25  per  cent).  The  isoelectric 
powdered  gelatin  was  put  into  200  c.c.  of  H20  or  a  solution  of 
different  concentrations  of  a  salt — NaCl,  CaCl2,  BaCl2,  CeCl3, 
or  Na2SO4 — and  containing  16  c.c.  of  0.1  N  HC1.  This  brought 
the  pH  of  the  micellae  down  to  2.8  or  less,  as  Tables  XXVI  to 
XXX  show.  The  powdered  gelatin  was  left  in  these  acid-salt 
solutions  for  two  hours  at  20°C.,  with  frequent  stirring.  Then 
the  supernatant  liquid  was  separated  from  the  powdered  particles 
of  gelatin  by  filtration  and  the  P.D.  between  the  micellae  and  the 
surrounding  liquid  (filtrate)  measured  with  the  Compton  electro- 
meter using  the  electrodes  described  in  Fig.  42.  After  this  the 
value  (pH  inside  —  pH  outside)  was  obtained  with  the  aid  of  the 
hydrogen  electrode  at  24°C.  and  this  value  multiplied  by  59  is 
called  the  calculated  P.D.  Tables  XXVI  to  XXX  give  the 
results.  The  uppermost  row  gives  the  nature  and  concentration 
of  the  salt.  The  next  row  gives  the  relative  volume  of  the  gel 
of  gelatin,  and  the  depressing  influence  of  the  salt  on  the  swelling; 
then  follow  the  values  for  pH  inside  and  outside  measured  with 
the  hydrogen  electrode  and  then  the  values  pH  inside  minus 
pH  outside.  The  last  two  columns  give  the  calculated  P.D. ,  i.e., 
the  value  59  (pH  inside  minus  pH  outside),  and  the  P.D.  observed 
with  the  Compton  electrometer  and  the  indifferent  electrodes 
described  in  Fig.  42. 

The  fact  in  common  to  all  the  experiments  is  the  satisfactory 
agreement  between  the  observed  and  calculated  P.D.  except  that 
the  calculated  P.D.  is  on  the  average  about  3  millivolts  higher 


160 


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162 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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than  the  observed  P.D.  and  the 
cause  for  this  difference  is  un- 
known at  present.  It  is,  how- 
ever, a  constant  difference  and 
has  therefore  no  relation  to  the 
nature  of  the  salt  used.  When 
we  use  as  a  standard  for  com- 
parison of  the  relative  depressing 
effect  of  a  salt  the  concentration 
required  to  depress  the  observed 
P.D.  to  about  10  millivolts,  we 
find  that  the  following  concen- 
trations of  the  five  salts  are 
required  for  this  purpose. 

NaCl  about  M/64 
CaCl2  slightly  above  M/128 
BaCl2  slightly  above  M/128 
CeCl3  between  M/256  and  M/128 
Na2SO4  about  M/256 

The  main  fact  is  that  the  de- 
pressing effect  of  the  four  salts 
NaCl,  CaCl2,  BaCl2,  and  CeCl3 
is  determined  by  the  chlorine  ion 
concentration,  and  that  the  val- 
ency of  the  cation  has  no  influ- 
ence. This  leaves  no  doubt  that 
the  charge  of  the  micellae  is  an 
unequivocal  function  of  the, 
Donnan  equilibrium. 

The  depressing  action  of  Na2- 
SO4  is  about  four  times  as  great 
as  that  of  NaCl. 

If  the  precipitating  effect  of  a 
salt  on  the  stability  of  colloidal 
suspensions  is  due  exclusively  to 
the  depressing  effect  of  the  salt 
on  the  P.D.  between  micellae  and 
surrounding  liquid,  only  that  ion 


THE  ELECTRICAL  CHARGES  OF  MICELLA  163 

should  have  an  effect  on  the  precipitation  which  has  the  opposite 
charge  to  that  of  the  micellae;  and  this  precipitating  effect  should 
increase  with  the  valency  of  the  active  ion.  The  Hardy-Schulze 
and  Linder-Picton  rule  of  precipitation  is,  therefore,  only  the 
consequence  of  the  Donnan  equilibrium. 

It  is  necessary  to  correct  in  this  place  an  error  which  occurs 
frequently  in  the  colloidal  literature,  namely,  the  statement  that 
in  the  precipitation  of  colloidal  suspensions  by  neutral  salts  the 
colloidal  particles  are  brought  to  the  isoelectric  point  by  the 
salt.  What  happens  is  that  by  the  addition  of  neutral  salts  the 
P.D.  between  suspended  particles  and  liquid  is  diminished,  and 
if  enough  salt  is  added  completely  annihiliated.  This  is  due  to 
the  fact  that  as  a  consequence  of  the  addition  of  the  salt  the  value 

y  in  the  term  log  ( 1  +  -j  ,  upon  which  the  P.D.  depends,  increases. 

When,  however,  the  gelatin  granules  are  brought  to  the  iso- 
electric point  of  gelatin,  i.e.,  to  pH  4.7,  through  a  change  in  the 
hydrogen  ion  concentration,  the  P.D.  between  particles  and 
surrounding  liquid  becomes  also  zero,  but  for  a  different  reason, 
namely,  because  the  gelatin  is  now  no  longer  ionized  at  this  point. 
In  this  case  the  P.D.  becomes  zero  because  z  in  the  term  log 

4-  -)  becomes  zero. 


If  the  theory  of  the  Donnan  equilibrium  is  applied  to  these 
phenomena  it  becomes  therefore  obvious  that  the  P.D.  between 
colloidal  particles  and  surrounding  liquid  can  become  zero  in  two 

different  ways :  first,  by  making  the  value  of  z  in  the  term  1  +  - 

equal  to  zero,  and  this  is  only  possible  by  bringing  the  hydrogen 
ion  concentration  of  the  solution  to  that  of  the  isoelectric  point 
of  the  protein  (which  in  the  case  of  gelatin  is  at  pH  4.7);  and 

second,  by  making  y  in  the  term  1  +  -  very  large,  i.e.,  by  increas- 
ing the  concentration  of  the  ions  having  the  opposite  sign  of 
charge  to  that  of  the  colloidal  particles,  and  this  can  be  done  at 
any  pH  by  adding  a  neutral  salt. 

It  is  therefore  entirely  wrong  to  say  that  the  salt  causes  the 
precipitation  of  the  suspended  particles  by  bringing  them  to  the 
isoelectric  point  or  that  the  isoelectric  point  of  a  protein  is  shifted 


164  THEORY  OF  COLLOIDAL  BEHAVIOR 

by  the  addition  of  a  salt.  The  isoelectric  point  of  a  protein  is  a 
constitutional  property  of  the  protein  which  need  not  be  and 
probably,  as  a  rule,  is  not  affected  by  the  addition  of  a  neutral 
salt,  since  it  is  that  hydrogen  ion  concentration  at  which  a  protein 
dissociates  equally  as  an  acid  and  as  a  base. 

Electrical  endosmose,  anomalous  osmosis,  and  kindred  phen- 
omena are  due  to  the  fact  that  there  is  a  P.D.  between  the  liquid 
and  the  walls  of  the  membrane  through  which  the  liquid  diffuses. 
It  is  often  assumed  that  this  P.D.  is  due  to  the  adsorption  of  ions 
by  the  membrane  whereby  the  charge  of  the  adsorbed  ion  is 
transferred  to  the  membrane.  The  writer  tested  this  idea  by 
experiments  with  membranes  which  had  received  a  coating  of  a 
protein.  He  found  that  at  the  isoelectric  point  of  the  protein 
which  forms  the  coating  no  electrical  transport  of  water  occurs 
either  in  electrical  endosmose  or  in  anomalous  osmosis.1  This 
agrees  with  the  idea  that  the  charge  of  the  liquid  inside  the  pores 
of  the  membrane  is  due  to  the  Donnan  equilibrium  between 
membrane  and  liquid. 

Experiments  on  anomalous  osmosis  were  made  to  test  the  idea 
whether  or  not  salts  can  transfer  an  electrical  charge  to  solid 
particles  of  gelatin  as  acids  or  alkalies  can.  In  order  to  test  this 
idea  these  experiments  were  made  with  liquids  of  pH  4.7,  i.e.,  at 
the  isoelectric  point  of  gelatin.  In  this  case  the  gelatin  is  not 
charged  through  acid  or  alkali  and  no  electrical  transport  of  water 
occurs  at  this  point  in  either  electrical  endosmose  or  in  anomalous 
osmosis.  If  now  a  salt,  like  CaCl2  or  Na2SO4,  were  able  to  trans- 
fer a  charge  to  the  gelatin,  this  should  betray  itself  by  an  electrical 
transport  of  water  through  the  gelatin  membrane  at  pH  4.7  in 
experiments  on  anomalous  osmosis.  It  was  found  that  salts,  like 
LiCl,  NaCl,  KC1,  MgCl2,  CaCl2,  BaCl2,  Na2S04,  and  others,  at 
pH  4.7,  leave  the  isoelectric  gelatin  uncharged,  and  that  no 
electrical  transport  of  liquid  occurs  at  pH  4.7  in  the  presence  of 
these  salts.  When,  however,  solutions  of  salts  with  trivalent 
cations,  such  as  LaCl3  or  CeCl3,  or  with  tetravalent  anion,  like 
Na4Fe(CN)6,  (all  of  pH  4.7)  were  used,  the  film  of  isoelectric 
gelatin  assumed  a  charge;  this  charge  was  positive  in  the  case  of 
CeCl3  or  LaCl3  and  negative  in  the  case  of  Na4Fe(CN)6.  It  was 

^OEB,  J.,  J.  Gen.  PhysioL,  vol.  2,  p.  557,  1919-20;  and  in  unpublished 
experiments. 


THE  ELECTRICAL  CHARGES  OF  MICELLAE  165 

apparently  not  due  to  a  change  in  the  pH  since  it  occurred  also 
when  the  salt  solution  was  buffered  by  the  addition  of  a  mixture 
of  Na  acetate  and  acetic  acid.1  Perrin  had  noticed  in  his  experi- 
ments on  electrical  endosmose2  that  salts  with  trivalent  cations 
reversed  the  sign  of  charge  of  negatively  charged  membranes  and 
that  tetravalent  anions  reversed  the  sign  of  charge  of  positively 
charged  membranes. 

As  a  possible  explanation  the  writer  suggested  a  loose  combina- 
tion between  isoelectric  gelatin  and  the  salts  with  trivalent  cations 
or  tetravalent  anions,  resulting  in  the  formation  of  complex  and 
positively  charged  gelatin-Ce  or  gelatin-La  ions  or  negatively 
charged  gelatin-Fe(CN)6  ions.  In  other  words,  salts  with 
trivalent  (and  tetravalent?)  cations  would  react  with  isoelectric 
gelatin  somewhat  like  acids,  and  salts  with  tetravalent  anions 
would  react  somewhat  like  alkalies,  the  former  causing  the  forma- 
tion of  positively  charged  complex  protein  ions,  the  latter 
causing  the  formation  of  negatively  charged  complex  protein 
ions, — with  this  difference,  that  the  protein-acid  salts  and  metal 
proteinates  are  much  more  stable  than  the  complex  salts  formed 
with  trivalent  cations  and  tetravalent  anions.  The  result  would 
in  both  cases  be  the  ionization  of  the  protein  salt,  resulting  in  a 
Donnan  equilibrium  and  P.D.  between  solid  protein  and  water. 

It  should  be  added  that  the  experiments  in  Chap.  II  show 
that  the  Ce  or  Fe(CN)6  ions  can  be  washed  away  very  easily,  so 
that  their  compounds  with  gelatin  differ  in  this  respect  from  the 
compounds  of  gelatin  with  acid  or  alkali. 

The  tendency  of  proteins  to  form  durable  films  when  in  contact 
with  solid  bodies  probably  explains  the  phenomenon  that  the 
addition  of  a  little  gelatin  keeps  coarser  particles  in  suspension 
which  without  the  gelatin  would  rapidly  settle.  If  in  this  case 
the  gelatin  forms  a  solid  film  on  the  surface  of  the  particle  the 
latter  will  assume  an  electrical  charge  as  long  as  the  liquid  has  a 
pH  different  from  4.7;  since  as  long  as  the  pH  is  either  less  or  more 
than  4.7  the  P.D.  between  water  and  the  gelatin-coated  particles 
will  keep  the  latter  from  settling.  When,  however,  the  pH  is 
4.7,  this  protective  influence  of  the  gelatin  must  disappear. 

iLoEB,  J.,  J.  Gen.  Physiol,  vol.  4,  p.  463,  1921-22. 
2  PERRIN,  J.,  /.  chim.  physique,  vol.  2,  p.  601,  1904;  vol.  3,  p.  50,  1905. 
Notice  sur  les  titres  et  travaux  scientifiques  de  M.  Jean  Perrin,  Paris,  1918. 


166  THEORY  OF  COLLOIDAL  BEHAVIOR 

It  is  very  interesting  that  this  film  formation  of  gelatin  on 
collodion  membranes  occurs  regardless  of  the  pH  of  the  solution. 
It  is,  therefore,  not  necessary  that  the  gelatin  (or  protein)  be 
ionized  to  form  a  film  on  collodion  membranes. 

Aside  from  the  electrical  charges,  the  osmotic  pressure  of  the 
solution  seems  also  to  have  an  effect  on  the  stability  of  the  col- 
loidal solution.  We  shall  see  that  the  Donnan  effect  demands  also 
that  the  osmotic  pressure  be  influenced  in  a  similar  way  by  the  pH, 
the  valency,  and  the  presence  of  salt  as  is  the  P.D.  The  depress- 
ing effect  of  the  salt  on  the  difference  of  osmotic  pressure  inside 
and  outside  the  micellae  may  possibly  be  of  more  importance  in 
the  precipitation  of  colloidal  suspensions  than  the  depressing 
effect  of  the  salt  on  the  electrical  charge  of  the  micellae.  This  is 
indicated  by  the  fact  that  the  difference  in  the  depressing  effect 
of  NaCl  and  Na2SO4  is  greater  for  osmotic  pressure  than  for  P.  D. 

6.  THE  ORIGIN  OF  THE  ELECTRICAL  CHARGES  OF  LIVING  CELLS 

AND  TISSUES 

In  his  first  paper  on  the  theory  of  membrane  equilibria  Donnan 
suggested  that  the  membrane  potentials  postulated  by  his  theory 
might  contribute  towards  an  explanation  of  the  action  of  nerves 
and  even  of  electrical  fish.  In  1911  the  writer  suggested  to  Dr. 
Beutner  that  he  investigate  the  P.D.  between  such  organs  as 
apples,  or  leaves  of  the  rubber  plant,  and  water,  instead  of  the  P.D. 
of  muscles  or  nerves,  which  had  usually  been  used  by  physiologists 
for  this  purpose.  In  these  experiments  Dr.  Beutner  made  the 
important  observation  that  the  P.D.  between  the  surface  of  an 
apple  or  a  leaf  was  a  maximum  when  the  bounding  liquid  was  pure 
water,  while  the  P.D.  was  depressed  when  a  salt  was  added  to 
the  water,  the  depressing  effect  on  the  P.D.  increasing  with  the 
concentration  of  the  salt.1  MacDonald2  had  observed  a  similar 
phenomenon,  namely,  the  increase  in  P.D.  between  nerve  and 
surrounding  salt  solution  with  increasing  dilution.  Donnan's 
theory  was  not  known  to  us  and  we  were  not  able  to  give  an 
explanation  of  the  depressing  effect  of  salt  on  the  P.D. 

A  search  was  made  for  those  substances  in  the  cortex  of  an 
apple  or  leaf  which  might  be  responsible  for  these  peculiar  con- 


,  J.  and  BEUTNER,  R.,  Biochem.-Z.,  vol.  41,  p.  1,  1912. 
2  MACDONALD,  J.  S.,  Proc.  Roy.  Soc.,  vol.  67,  p.  310,  1900. 


THE  ELECTRICAL  CHARGES  OF  MICELLA  167 

centration  effects  on  the  P.D.  When  the  P.D.  between  solid 
gels  of  gelatin  and  of  coagulated  egg  albumin  and  water  was 
investigated,  no  potential  differences  were  observed,  to  the  great 
surprise  and  disappointment  of  the  writer,  who  had  hoped  that 
the  investigations  of  the  P.D.  might  lead  to  an  explanation  of  the 
antagonistic  ion  effects  in  which  he  was  then  interested.  It  is 
possible  that  the  negative  results  with  protein  were  due  to  the 
fact  that  the  measurements  were  accidentally  made  near  the 
isoelectric  point.  On  the  other  hand,  it  was  found  that  there 
existed  a  P.D.  at  the  boundary  of  lipoids  (lecithin  dissolved  in 
guaiacol)  which  was  depressed  by  the  addition  of  salts  and  the 
more  the  higher  the  concentration  of  the  salt.1 

This  analogy  between  lipoids  and  living  cells  gave  us  the  im- 
pression that  the  proteins  had  no  share  in  the  potential  differ- 
ences observed  between  living  tissues  or  living  cells  and  watery 
solutions.  The  experiments  recorded  in  this  chapter  leave  no 
doubt  that  this  conclusion  was  wrong;  any  ion  in  a  cell  or  on  its 
surface  which  cannot  diffuse  into  the  surrounding  watery  solu- 
tion (no  matter  whether  the  ion  is  a  protein  or  a  fatty  acid  or  some 
complicated  lipoid  or  a  complicated  carbohydrate  or  even  a 
crystalloid)  can  or  must  give  rise  to  a  P.D.  which  is  depressed 
when  a  diffusible  salt  is  added  to  the  surrounding  watery  solution. 

The  idea  that  lipoids  are  the  substances  responsible  for  the 
P.D.  of  tissues  led  Beutner  to  an  extensive  and  most  interesting 
investigation  of  the  P.D.  at  the  boundary  of  water-immiscible 
substances  and  water.2  He  found  always  a  depressing  effect 
of  the  addition  of  salt.  Beutner  tried  to  explain  this  on  the 
basis  of  differences  in  the  electrolytic  dissociation  in  the  watery 
and  the  water-immiscible  (oily)  phase.  Such  an  explanation 
cannot  be  applied  to  the  experiments  with  protein  solutions  and 
yet  these  latter  solutions  also  show  the  depressing  effect  of  the 
addition  of  salt  on  the  P.D.  in  a  most  striking  way.  In  this 
latter  case  the  depressing  effect  of  the  salt  on  the  P.D.  is  due  to 
the  Donnan  equilibrium,  and  there  is  no  reason  why  the  theory 
of  membrane  equilibria  should  not  apply  to  the  P.D.  between 


,  J.  and  BEUTNER,  R.,  Biochem.-Z.,  vol.  51,  p.  288,  1913;  vol.  59, 
p.  195,  1914. 

2  BEUTNER,  R.,  "Die  Entstehung  elektrischer  Strome  in  lebenden  Gewe- 
ben,"  Stuttgart,  1920. 


168  THEORY  OF  COLLOIDAL  BEHAVIOR 

oily  and  watery  phases,  since  this  theory  only  demands  that  one 
ion  of  the  oily  phase  should  be  prevented  from  migrating  into 
the  watery  phase.  Any  lipoid  ion  would  fulfill  this  postulate 
of  the  theory.  The  peculiarities  of  electrolytic  dissociation 
found  by  Beutner  in  non-aqueous  solutions  must,  however,  influ- 
ence the  Donnan  equilibrium  in  a  secondary  way,  since  this 
equilibrium  depends  upon  ionization. 


CHAPTER  X 

OSMOTIC  PRESSURE1 

1.  THEORETICAL  STATEMENTS 

The  characteristic  features  of  colloidal  behavior  appear  also  in 
the  case  of  the  osmotic  pressure  of  solutions  of  protein  salts. 
If  the  Donnan  equilibrium  is  actually  the  cause  of  this  behavior, 
as  the  experiments  on  membrane  potentials  suggest,  it  must  be 
possible  to  derive  these  features  of  the  osmotic  pressure  quanti- 
tatively and  mathematically  from  Donnan's  equilibrium  formula. 
It  is  the  purpose  of  this  chapter  to  show  that  this  is  possible  on 
the  basis  of  van't  Hoff's  theory  of  osmotic  pressure.  The 
methods  of  measuring  the  osmotic  pressure  have  been  described 
in  Chap.  V.  Collodion  bags,  of  a  volume  of  about  50  c.c.,  are 
filled  with  a  protein  solution,  while  the  outside  solution  is  350  c.c. 
of  water  into  which  diffuses  some  of  the  free  acid  of  the  protein- 
acid  salt  solution  or  some  of  the  free  alkali  of  the  metal  proteinate 
solution.  In  order  to  hasten  the  establishment  of  equilibrium 
between  inside  and  outside,  the  pH  of  the  outside  solution 
was  usually  at  the  beginning  of  the  experiment  brought  to  the 
same  pH  as  that  of  the  protein  solution  by  adding  the  same  acid 
or  the  same  base  as  that  of  the  protein  solution.  Equilibrium 
was  established  after  about  6  hours  but  the  measurements  were 
usually  taken  after  about  20  hours.  The  solutions  were  kept  at 
a  constant  temperature  of  24°C.  throughout  the  experiment. 

A  gelatin  chloride  solution  contains  free  hydrochloric  acid, 
gelatin  chloride  (which  dissociates  electrolytically  like  any  other 
salt  in  watery  solution),  and  non-ionogenic  protein  molecules. 
A  1  per  cent  gelatin  chloride  solution  of  about  pH  3.5  is  in  equi- 
librium with  a  HC1  solution  (free  from  protein)  of  a  pH  of  about 
3.0,  the  solutions  being  separated  by  a  collodion  membrane. 

The   terms  for  the   calculation   of  the   osmotic   pressure    of 
gelatin  solutions  are  the  same  as  those  used  by  Procter  (1914) 
,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  691,  1920-21. 
169 


170  THEORY  OF  COLLOIDAL  BEHAVIOR 

and  by  Procter  and  Wilson  (1916) l  for  the  calculation  of  the 
swelling  (see  Chap.  XI).  Since,  however,  the  application  of 
the  theory  is  simpler  in  the  case  of  osmotic  pressure  than  in  the 
case  of  swelling,  it  may  be  well  to  discuss  osmotic  pressure 
experiments  first.2 

Let  y  be  the  concentration  of  the  H  and  Cl  ions  of  the  free  HC1 
inside  a  gelatin  chloride  solution  (containing  1  gm.  of  originally 
isoelectric  gelatin  in  100  c.c.),  z  the  concentration  of  the  Cl  ions 
held  by  the  gelatin  ions,  and  a  the  sum  of  the  concentrations  of 
the  gelatin  ions  and  non-ionized  molecules  of  gelatin.  For  the 
sake  of  simplification  we  assume  complete  electrolytic  dissociation 
of  the  gelatin  chloride  and  of  the  HC1.  In  this  case  the  osmotic 
pressure  of  the  inside  solution  is  determined  by 

2y  +  z  +  a 

Since,  however,  the  outside  solution  is  at  equilibrium  not  H2O 
but  HC1  solution — in  the  example  selected  a  HC1  solution  of 
about  pH  3.0 — the  observed  osmotic  pressure  is  the  difference 
between  the  osmotic  pressure  of  the  inside  solution  and  the 
osmotic  counterpressure  of  the  outside -solution. 

Let  x  be  the  concentration  of  the  H  ions  in  the  outside  solution, 
then  the  osmotic  counterpressure  of  the  outside  solution  is 
determined  by  2x. 

Hence  the  observed  osmotic  pressure  of  the  gelatin  chloride 
solution  is  determined  by 

2y  +  z  +  a  -  2x 

The  osmotic  pressure  is  observed  experimentally,  y  can  be 
calculated  from  the  pH  inside,  and  x  from  the  pH  outside. 
z  can  be  calculated  from  Donnan's  equilibrium  equation 

x2  =  y(y  +  z}  (1) 

(x  +  y)(x  -y) 

y 

where  x,  y,  and  z  have  the  significance  stated  above.  The  z 
thus  calculated  differs,  however,  from  the  z  obtained  from  the 

1  PROCTER,  H.  R.,  J.  Chem.  Soc.,  vol.  105,  p.  313,  1914.     PROCTER,  H.  R. 
and  WILSON,  J.  A.,  J.  Chem.  Soc.,  vol.  109,  p.  307,  1916. 
2LoEB,  J.,  J.  Gen.  Physiol,  vol.  3,  p.  691,  1920-21. 


OSMOTIC  PRESSURE  171 

titration  values,  and  this  is  probably  the  cause  of  a  slight  dis- 
crepancy between  observed  and  calculated  osmotic  pressures. 
For  the  present  we  calculate  z  from  equation  (1). 

a  is  unknown,  and  we  therefore  can  only  calculate  for  the 
present  the  values  of 

2y  +  z  -  2x 

If  we  express  the  theoretical  osmotic  pressure  of  a  grammolecu- 
lar  solution  in  terms  of  millimeter  pressure  of  a  column  of  H2O  we 
get  (with  correction  for  a  temperature  of  24°C.) 


22.4  X  760  X  13.6  X          =  2.5  X  105  mm. 


In  other  words,  a  theoretical  pressure  of  2.5  mm.  H^O  cor- 
responds to  a  concentration  of  10~5  N.  In  the  following  tables 
all  concentrations  are  expressed  in  terms  of  10~5  N  and  hence  we 
only  need  to  multiply  the  values  for  2y  +  z  —  2x  given  in  our 
tables  by  2.5  to  obtain  the  calculated  osmotic  pressure  of  the 
gelatin  solution  in  mm.  H2O  (neglecting  the  osmotic  pressure  of 
the  gelatin  ions  and  molecules). 

Equation  (1)  holds  in  the  case  of  solutions  of  all  gelatin-acid 
salts  with  monovalent  anion;  i.e.,  gelatin  chloride,  acetate, 
phosphate,  tartrate,  citrate,  etc.  When,  however,  the  anion  of 
a  gelatin-acid  salt  is  divalent,  as  in  the  case  of  gelatin  sulphate, 
the  equilibrium  equation  becomes  one  of  the  third  degree,  as 
has  been  stated  in  Chap.  VIII.  If  x  is  the  hydrogen  ion  con- 
centration of  the  outside  solution,  the  concentration  of  the  SO4 

ions  in  the  outside  solution  becomes  ~-     If  y  is  the  concentration 

of  the  H  ions  of  the  free  sulphuric  acid  in  the  inside  solution,  | 

is  the  concentration  of  the  SO4  ions  of  the  free  acid  inside  the 
gelatin  sulphate  solution.  In  the  case  of  gelatin  chloride  z  repre- 
sented the  concentration  of  chlorine  ions  in  combination  with 

the  gelatin;  hence  ~  will  represent  the  concentration  of  864  ions 
in  combination  with  the  same  number  of  gelatin  ions. 


172  THEORY  OF  COLLOIDAL  BEHAVIOR 

The  equilibrium  equation,  therefore,  assumes  in  the  case  of 
gelatin  sulphate  the  following  form: 


From  equation  (2)  it  follows  that 

9  —  x  ~  y 
~¥~ 

The  osmotic  pressure  of  the  gelatin  sulphate  solution  should 
therefore  be  calculated  from  the  following  values  (omitting  the 
share  of  the  osmotic  pressure  due  to  the  gelatin  molecules  and 
ions). 

3      ,    z      3 


2.  THE  CALCULATED  CURVES  FOR  THE  INFLUENCE  OF  pH  AND 

VALENCY 

Solutions  containing  1  gm.  of  originally  isoelectric  gelatin  in 
100  c.c.  and  containing  different  quantities  of  acid  were  prepared. 
Collodion  bags  cast  in  the  form  of  Erlenmeyer  flasks  of  50  c.c. 
volume  were  filled  with  the  1  per  cent  solutions  of  a  gelatin-acid 
salt  and  put  into  beakers  containing  350  c.c.  of  H2O.  In  order 
to  accelerate  the  establishment  of  the  equilibrium  between  inside 
and  outside  solutions  a  certain  amount  of  acid  was  added  to  the 
outside  water  (e.g.,  HC1  in  the  experiments  with  gelatin  chloride, 
H3PO4,  in  the  experiments  with  gelatin  phosphate,  etc.).  Each 
Erlenmeyer  flask  was  closed  with  a  rubber  stopper  perforated 
by  a  glass  tube  serving  as  a  manometer.  All  this  was  described 
in  more  detail  in  Chap.  V. 

In  Fig.  43  are  plotted  the  values  of  the  osmotic  pressures  of  1 
per  cent  solutions  of  gelatin  chloride,  gelatin  phosphate,  and 
gelatin  sulphate,  calculated  on  the  basis  of  equations  (1)  and  (2); 
and  Tables  XXXI,  XXXII,  and  XXXIII  give  the  data  on  the 
basis  of  which  the  calculations  are  made.  The  abscissae  in 
Fig.  43  are  the  pH  in  the  inside  solution  at  the  point  of  equilib- 
rium, the  ordinates  are  the  values  for  osmotic  pressure  calcu- 
lated from  the  equations  referred  to.  Figure  44  gives  the 
actually  observed  osmotic  pressures  in  the  same  experiments 
which  furnished  the  data  for  the  calculated  curves  in  Fig.  43. 
The  reader  will  notice  that  the  three  curves  plotted  in  Fig.  43 


OSMOTIC  PRESSURE 


173 


show  not  only  the  same  qualitative  characteristics  as  the  curves 
for  the  observed  osmotic  pressures  in  Fig.  44,  but  show  them 
almost  quantitatively;  except  that  a  correction  for  the  value  of 
osmotic  pressure  due  to  the  gelatin  particles  themselves  has  to  be 
added,  a  point  which  will  be  discussed  later.  What  is  of  im- 


pH  1.4  1.6  IS  20  22  2.4  2.6  2.8  3.0  32  3.4  a6  3.8  4.0  42  44  4.6  4fi 

FIG.  43. — Calculated  curves  of  osmotic  pressure  taken  from  the  data  of  the 
experiments  represented  in  Fig.  44.  The  calculation  is  made  on  the  basis  of  the 
validity  of  Donnan's  theory  of  membrane  equilibrium.  The  calculations  lead  to 
curves  resembling  the  curves  in  Fig.  44  in  all  essential  points,  in  regard  to  valency 
effect  of  the  anion,  as  well  as  in  regard  to  influence  of  pH  (see  legend  under 
Fig.  44). 

portance  here  is  the  following :  The  curves  for  osmotic  pressure 
calculated  on  the  basis  of  the  Donnan  equation  and  plotted  in 
Fig.  43  resemble  the  curves  for  the  osmotic  pressure  observed  in 
the  same  experiments  represented  in  Fig.  44  in  the  following 
essential  points. 


174 


THEORY  OF  COLLOIDAL  BEHAVIOR 


(a)  The  curve  for  the  calculated  osmotic  pressure  of  gelatin 
chloride  is  identical  with  the  curve  for  the  calculated  osmotic 
pressure  of  gelatin  phosphate,  and  the  same  is  true  for  the  two 
corresponding  curves  representing  the  observed  osmotic  pressures 
(Figs.  43  and  44). 


450 
425 
400 
375 
G)  350 

5J325 

Ssoo 

:g  250 
g  225 
0  200 
*§  175 
I  150 
S  125 
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75 
50 
25 
0 

. 

/ 

*~ 

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\*r 

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/ 

A 

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^ 

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pH  1.4  1.6   IB  2.0   22  2.4  2.6  2.8  3.0  3.2  3.4  3.6  3.8  40  42  4.4  46  45 

FIG.  44. — Observed  curves  representing  the  influence  of  pH  and  valency  of 
anion  on  osmotic  pressure  of  solutions  in  gelatin-acid  salts  containing  1  gm.  of 
originally  isoelectric  gelatin  in  100  c.c.  solution.  The  curves  for  gelatin  chloride 
and  gelatin  phosphate  are  identical  since  the  anions,  Cl  and  HzPC^,  of  these  two 
gelatin  salts  are  monovalent.  The  curve  for  gelatin  sulphate  is  less  than  half  as 
high  as  the  curve  for  the  two  other  salts  because  the  anion  of  gelatin  sulphate  is 
bivalent.  Both  curves  rise  from  the  isoelectric  point  at  4.7  to  a  maximum  at  pH 
about  3.4  or  3.5,  and  then  drop  rapidly  again. 

(6)  The  curve  for  the  calculated  osmotic  pressure  of  gelatin 
sulphate  is  a  little  less  than  half  as  high  as  the  curves  for  the  calcu- 
lated osmotic  pressures  of  gelatin  chloride  and  gelatin  phosphate; 
and  the  same  is  true  for  the  curves  representing  the  observed 
osmotic  pressures  of  gelatin  sulphate  and  gelatin  chloride. 


OSMOTIC  PRESSURE 


175 


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176 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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(c)  All  the  curves  in  Figs. 
43  and  44  rise  from  a  minimum 
at  pH  4.7,  reach  a  maximum 
(which  lies  at  pH  3.4  or  3.5 
for  the  observed,  and  at  3.0 
for  the  calculated  curves),  and 
then  drop  again  as  steeply  as 
they  rose  on  the  other  side. 
Moreover,  the  absolute  values 
of  observed  and  calculated 
osmotic  pressures  are  almost 
equally  high,  a  fact  which  will 
be  discussed  more  fully  a  little 
further  on. 

It  may  be  added  that  the 
curve  for  the  calculated  val- 
ues of  the  osmotic  pressure 
of  gelatin  oxalate  solutions 
agrees  also  with  the  curve  for 
the  observed  values  of  the 
osmotic  pressure  of  solutions 
of  the  same  gelatin  salt, 
both  being  slightly  lower 
than  the  curves  for  gelatin 
chloride. 

In  comparing  the  observed 
with  the  calculated  values  for 
osmotic  pressure,  the  reader 
must  keep  in  mind  that  the 
differences  are  exaggerated  on 
account  of  the  fact  that  the 
pressures  are  expressed  in 
millimeters  of  a  column  of 
water  instead  of  mercury. 
If  we  had  expressed  all  the 
figures  in  terms  of  pressure  of 
mercury,  as  is  customary,  the 
agreement  would  have  ap- 
peared more  complete. 


OSMOTIC  PRESSURE 


177 


We  can,  therefore,  say  that  (with  the  exception  of  two  minor 
discrepancies  to  be  discussed  further  on)  the  Donnan  equilibrium 
accounts  not  only  qualitatively  but  almost  quantitatively  for 
(a)  the  valency  effect  of  the  anion  with  which  the  gelatin  is  in  com- 
bination; (b)  for  the  effect  of  the  pH. 


s 


450 
425 
400 
375 
350 
325 
300 
275 
250 


£  225 

a  200 

t/2 

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150 

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100 

75 

50 

25 


t- 


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\ 


\ 


pH  1.6   IB  20   2.2  2.4  26  2.8  3.0   3.2  34  3.6   3.8  4.0  4.2  4.4  4.6 

FIG.  45. — Showing  agreement  and  minor  discrepancies  between  the  curves 
of  observed  and  calculated  osmotic  pressures  of  1  per  cent  gelatin  chloride 
solutions. 

A  glance  at  the  formulae  will  show  us  that  this  influence  of 
the  pH  on  osmotic  pressure  te  a  mathematical  consequence  of 
12 


178  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  theory.     From  the  equilibrium  equation,  x2  —  y(y  +  z),  it 
follows  that 


s  =  Vy(y  +  2) 

If  we  substitute  this  value  in  the  term  for  osmotic  pressure  2y 
-\-z-2x,  we  get 


2y  +  z  -  2Vy(y+  z) 

When  z  is  zero  (at  the  isoelectric  point),  the  whole  term  becomes 
zero.  At  the  isoelectric  point  we  observe  therefore  the  osmotic 
pressure  of  the  protein  solution  free  from  the  disturbing  effects 
of  the  Donnan  equilibrium.  When  we  add  acid  to  isoelectric 
gelatin,  z  increases  and  so  does  y,  but,  as  we  have  shown  in 
Table  XIV  of  Chap.  VIII,  z  increases  at  first  more  rapidly 
than  y  and  later  more  slowly.  Hence,  the  value  of  2y  +  z  — 


+  «),  i.e.j  the  osmotic  pressure,  increases  at  first  the  more 
acid  we  add  to  isoelectric  gelatin  until  a  maximum  is  reached. 
When.?/  grows  more  rapidly  than  z,  z  becomes  more  and  more 
negligible  in  comparison  to  y  and  the  value  of  the  term  2y  +  z  — 
2-\/y(y  -J-  z)  diminishes  again  with  increasing  y,  finally  approach- 
ing zero  again  as  a  limit. 

The  curves  representing  the  values  for  calculated  osmotic 
pressures  differ  in  one  or  two  respects  from  the  curves  represent- 
ing the  values  for  the  observed  osmotic  pressures  (Fig.  45).  As 
a  rule,  the  calculated  values  are  lower  than  the  observed  values 
(though  this  is  only  partly  true  for  Fig.  45).  This  is  to  be  ex- 
pected since  the  calculated  curves  do  not  include  that  part  of  the 
osmotic  pressure  which  is  due  to  the  protein  particles  and  the 
calculated  curves  must  therefore  be  too  low,  though  this  is 
(perhaps  accidentally)  not  true  for  the  descending  part  of  the 
curve  (for  lower  pH)  in  Fig.  45.  The  slight  discrepancies  be- 
tween observed  and  calculated  values  may  be  due  to  an  uncer- 
tainty in  our  calculations  or  to  a  simplification  in  our  assumption 
which  is  not  justified.  We  assume,  e.g.,  complete  electrolytic 
dissociation  of  all  compounds,  which  may  not  be  entirely  correct. 

The  discrepancies  may  also  be  due  to  an  error  in  calculating  z. 

f7/*  r  I    77  ji'y*  -^  77) 

We  calculated  z  from   —  —    where   x   and   y   were 

y 

the  hydrogen  ion  concentrations  determined  electrgmetricaily. 


OSMOTIC  PRESSURE 


179 


There  is  a  second  way  of  measuring  z,  namely,  by  determining 
the  concentration  of  Cl  inside  a  1  per  cent  gelatin  chloride  solu- 
tion by  titration.  The  Cl  inside  is  partly  in  combination  with  H 
(free  HC1)  and  partly  combined  with  gelatin.  By  titrating  with 
NaOH  to  pH  7.0  and  making  the  correction  for  isoelectric 
gelatin  (as  described  in  Chap.  IV)  we  determine  the  value 
z  -f-  y.  y  is  known  from  the  pH  and  by  deducting  y,  we  get  z. 
We  made  such  determinations  at  the  end  of  an  osmotic  experi- 

f  y)(x-y) 


ment  and  calculated  z  also  from 


y 


in  the    same 


experiment.     Table  XXXIV  gives  a  comparison  of  the  values 
of  z  obtained  in  identical  solutions  by  the  two  different  methods. 

TABLE  XXXIV.— CONCENTRATIONS  OF  z  X  105  N 


pH  of  gelatin  solu- 
tion            .  .    . 

4  51 

4  26 

3  96 

3  61 

3  53 

3  32 

3  23 

2  86 

2  32 

2  16 

1  93 

z  calculated  from 

(x  +  y}  (x  —  y) 

30 

90 

166 

223 

252 

316 

387 

493 

570 

687 

687 

y 

z  found  by  titra- 
tion   

17 

84  5 

170 

275 

291 

342 

401 

532 

548 

838 

885 

There  is  no  wide  divergence  between  the  two  sets  of  values, 
yet  enough  to  suggest  that  the  calculated  values  of  z  may  be 
chiefly  responsible  for  the  discrepancy  between  calculated  and 
observed  curves.  The  reader  must  remember  that  the  value  of 
z  is  multiplied  by  2.5  in  the  calculations  of  the  osmotic  pressure 
(and,  therefore,  any  error  in  the  calculated  osmotic  pressure  is 
multiplied  in  the  same  way). 


3.  THE  INFLUENCE  OF  THE  ADDITION  OF  SALTS 

It  was  first  pointed  out  by  R.  S.  Lillie  that  the  addition  of  salt 
to  a  gelatin  solution  depresses  its  osmotic  pressure.  It  should, 
however,  be  stated  that  this  depressing  effect  does  not  occur  at 
the  isoelectric  point.  When  we  add  different  salts  to  a  gelatin 
chloride  solution  of  an  initial  pH  3.5  containing  1  gm.  originally 
isoelectric  gelatin  in  100  c.c.  solution,  the  depressing  effect  of  the 
salt  on  osmotic  pressure  should  according  to  the  Donnan  equa- 


180 


THEORY  OF  COLLOIDAL  BEHAVIOR 


tion  be  due  to  the  anion;  and  this  is  the  case,  as  Fig.  46  shows. 
The  gelatin  chloride  solutions  were  made  up  in  different  concen- 
trations of  the  salts,  NaCl,  NaNO3,  CaCl2,  and  Na2SO4.  The 
pH  of  the  mixtures  was  always  3.5.  Collodion  bags  of  a  volume 


M. 
8 


M.  _M    M.  M 

128   64    3Z    16     8      4 

Concentration  of  salts 

FIG.  46. — Depressing  effect  of  neutral  salts  on  the  osmotic  pressure  of  a  1  per  cent 
solution  of  gelatin  chloride  of  pH  3.5. 


of  about  50  c.c.  were  filled  with  the  gelatin  chloride-salt  mixtures. 
These  bags  were  dipped  into  beakers  containing  350  c.c.  of  a 
solution  of  the  same  inorganic  salt  of  the  same  concentration 
as  that  contained  in  the  gelatin  solutions,  but  these  outside 
solutions  contained  no  gelatin.  The  pH  of  the  outside  solutions 


OSMOTIC  PRESSURE  181 

was  made  at  the  beginning  3.0  to  accelerate  the  establishment 
of  the  equilibrium.  The  osmotic  pressure  was  read  after  about 
20  hours.  The  temperature  was  (as  always  in  these  cases) 
24°C. 

In  Fig.  46  the  abscissae  are  the  initial  concentrations  of  the  salt 
solutions  while  the  ordinates  are  the  osmotic  pressures.  The  Don- 
nan  equilibrium  caused  a  change  of  pH  as  well  as  of  the  dis- 
tribution of  the  neutral  salts  on  the  opposite  sides  of  the 
membrane.  The  change  of  pH  in  this  experiment  has  already 
been  discussed  in  Tables  XVIII,  XIX,  and  XX  of  Chapter 
VIII.  Figure  46  shows  that  the  depressing  effect  of  NaCl  and 
NaN03  is  practically  the  same,  that  the  depressing  effect  of  an 
equimolecular  concentration  of  CaCl2  is  not  very  far  from  twice 
as  great  as  that  of  NaCl,  but  that  the  effect  of  Na2SO4  —  where 
the  anion  is  bivalent  —  is  about  eight  times  as  great  as  that  of  a 
NaCl  solution  of  the  same  molecular  concentration.  This  leaves 
no  doubt  that  the  depressing  effect  is  due  to  the  anion  and  that 
the  cation  is  seemingly  without  any  influence  (it  has  certainly 
not  any  influence  in  the  opposite  direction  from  that  of  the 
anion).  This  depressing  influence  of  the  anion  of  a  neutral  salt 
on  the  osmotic  pressure  of  protein-acid  salts  can  be  derived  from 
the  Donnan  equilibrium  equation. 

Omitting  that  share  of  the  osmotic  pressure  of  the  solution 
which  is  due  to  the  protein  molecules  and  ions,  the  share  due  to  the 
Donnan  equilibrium  is  expressed  by  the  term 

2y  +  z  -  2Vy(y  +  z)  (1) 

Suppose  the  gelatin  be  gelatin  chloride  and  the  salt  added  NaCl. 
Then  z  is  the  concentration  of  Cl  in  combination  with  gelatin, 
while  y  is  the  sum  of  the  concentration  of  the  Cl  ions  combined 
with  the  H  ions  of  the  free  HC1  present  in  the  gelatin  solution 
and  the  Cl  ions  of  the  NaCl  contained  in  the  gelatin  solution  at 
equilibrium.  We  can  ascertain  the  total  concentration  of  Cl 
ions  inside  the  gelatin  solution,  i.e.,  the  value  of  y  +  z  in  term 
(1)  by  tit  ration.  This  term  2y  -\-  z  —  2\/y(y  +  z)  will  become 
the  smaller,  the  more  closely 


approaches  the  value  1. 


182  THEORY  OF  COLLOIDAL  BEHAVIOR 

It  is  obvious  that  if  z  is  small  and  constant,  while  y  increases 
more  and  more  (through  the  addition  of  NaCl),  z  becomes  a 
negligible  quantity  and  the  term 

a  2y 

approaches  /—  =  1 


0    7-7 
2Vy(y 


We  can  measure  the  term  \/y(y  +  z)  directly  by  titrating  the 
outside  solution  for  Cl.  We  cannot  determine  2y  -f  z  directly 
but  we  can  determine  y  +  z  by  titrating  the  inside  solution  for 
Cl.  If  both  tit  rations  are  made  after  equilibrium  is  established 
we  get  the  value  of 


2) 

and  the  variations  of  this  value  with  increasing  concentration  of 
NaCl  are  contained  in  Table  XXXV.  It  is  seen  that  this  value 
is  almost  1  when  the  NaCl  solution  is  M/32. 

Now  the  value  of  —  /       '      =  does  not  differ  much  from  the 

Vy(y+*) 

value  -  —  /  ;  as  long  as  y  is  large  in  comparison  with  2,  and 


we  can  say  that  with  z  small  and  constant  and  y  large  and  increas- 
ing rapidly,  the  two  values 

y  +  z  2y  +  z 


approach  the  value  1  almost  (but  not  quite)  at  an  equal  rate. 
Hence,  it  follows  from  Table  XXXV  that  if  the  concentration  of 
NaCl  becomes  M/32  the  value  2y  +  z  —  2VtKi  +  2)  must  be 
nearly  zero.  In  this  case  the  osmotic  pressure  of  the  1  per  cent 
gelatin  chloride  solution  must  be  almost  but  not  quite  down  to 
that  of  the  pure  gelatin  solution  as  it  is  at  the  isoelectric  point. 
The  actual  observations  plotted  in  Fig.  46  show  that  for  M/32 
NaCl  or  M/32  NaNO3  a  1  per  cent  solution  of  gelatin  chloride 
of  pH  about  3.5  has  an  osmotic  pressure  not  far  from  that  of 

y  -\-  z 

isoelectric  gelatin.     If  the  values  of      /  ==  are  plotted  as 

V  y(y  +  z) 


OSMOTIC  PRESSURE 


183 


ordinates  over  the  values  of  the  concentration  of   NaCl  it  is 
noticed  that  the  two  curves  are  approximately  parallel  (Fig.  47). 


400 
375 
350 
325 
300 

d  250 

S  225 
^-200 

?..» 

100 
75 
50 
25 
0 

2.8 
2.6 
2.4 
2.2 
2.0 
1.8 
1.6 
1.4 
1.2 
1.0 

\ 

• 

\ 

i 

\ 

\ 

V 

L 

\i 

? 
i 

( 

m 

V 

S 

\ 

G 

X 

' 

Av       \ 

^ 

a 

\ 

u 

V 

\ 

^ 

\ 

s 

^, 

{ 

\ 

H 

Si 

>    . 

KM    MMMUMM 
2018  1524  512  256  128  64    32  IF 

Concentration  of  NaCl 

Fia.    47. — Parallelism    between    depressing    action  of  NaCl  in  the  osmotic 
pressure  of  a  gelatin  chloride  solution  and  the  curve  representing  the  value 


This  shows  that  the  Donnan  equation  actually  accounts  for  the 
depressing  effect  of  neutral  salts  on  the  osmotic  pressure  of  a 
gelatin  chloride  solution, 


184 


THEORY  OF  COLLOIDAL  BEHAVIOR 


TABLE  XXXV. — INFLUENCE   OF   NaCl   ON   OSMOTIC  PRESSURE  OF  1  PER 
CENT  GELATIN  CHLORIDE  SOLUTION 


Concentration 
of  NaCl 

Inside 

y  +  z 

Outside 

Vy(y  +z] 

y  +  2 

Vy(y  +  z) 

M/2,048 

566 

200 

2.83 

M/1,024 

633 

267 

2.37 

M/512 

(800 

300 

2.66) 

M/256 

966 

534 

1.81 

M/128 

1,370 

1,000 

1.37 

M/32 

3,800 

3,340 

1.14 

M/16 

6,930 

6,540 

1.06 

4.  THE   INFLUENCE   OF   THE   CONCENTRATION   OF   A   PROTEIN 
SOLUTION  UPON  THE  OSMOTIC  PRESSURE 

An  increase  in  the  concentration  of  a  protein  solution  at  the 
same  pH  and  in  the  absence  of  neutral  salts  should  have  a 
double  effect  on  the  osmotic  pressure.  It  should,  first,  raise  the 
osmotic  pressure  of  the  solution  on  account  of  the  increase  in  the 
number  of  protein  particles  in  the  solution;  and  it  should,  second, 
lead  to  a  further  increase  in  osmotic  pressure  due  to  an  increase 
in  the  value  of  2y  +  z  —  2x  or  2y  +  z  —  2\/y(y  +  z),  for  it  is 
obvious  that  as  long  as  y  is  constant,  i.e.,  at  constant  pH  of  the 
gelatin  solution,  the  value  of  the  term  2y  -f  z  —  2\/y(y  -f  z) 
will  increase  with  increasing  z.  The  two  effects  can  be  separated 
by  subtracting  the  value  of  the  term  2y  +  z  —  2x  from  the 
observed  osmotic  pressure.  The  difference  between  the  two 
values  should  (within  the  limits  of  the  accuracy  of  the  experi- 
ments) increase  with  the  concentration  of  the  protein.  Both 
expectations  are  fulfilled. 

Different  concentrations  of  gelatin  phosphate  from  2  per  cent  to 
0.5  per  cent  were  prepared,  all  having  a  pH  of  3.5.  The  gelatin 
phosphate  solutions  were  put  into  encollodion  flasks  of  50  c.c. 
volume,  each  connected  with  a  glass  tube  serving  as  a  manometer 
as  described,  and  these  flasks  were  put  into  beakers  containing 
350  c.c.  of  H2O,  the  pH  of  which  was  brought  at  the  beginning  of 
the  experiment  to  3.5  through  the  addition  of  H3PO4.  When  the 
bags  containing  gelatin  phosphate  solutions  are  put  into  water 


OSMOTIC  PRESSURE  .    185 

the  latter  diffuses  rapidly  into  the  gelatin  solution  thereby 
lowering  the  concentration  of  the  gelatin  solution.  To  avoid 
this  error  so  much  gelatin  phosphate  solution  was  poured  into 
each  bag  and  glass  tube  that  at  the  beginning  of  the  experiment 
the  liquid  reached  already  to  about  that  level  which  from  pre- 
ceding experiments  we  knew  the  gelatin  solution  would  reach 
in  the  manometer  at  the  point  of  osmotic  equilibrium.  All 
experiments  were  made  in  duplicate.  In  addition  to  the  osmotic 
pressure  we  measured  the  pH  inside  and  outside  after  equilibrium 
was  reached.  From  these  latter  data  the  osmotic  pressure  due 
to  the  H  and  H2PO4  ions  could  be  calculated,  being  equal  to 

(2y  +  z  -  2x)  X  2.5  mm.  H2O 

By  deducting  this  value  from  the  observed  osmotic  pressure  in 
each  case  it  was  hoped  to  obtain  a  rational  value  for  the  share 
of  the  protein  particles  in  the  observed  osmotic  pressure.  Table 
XXXVI  gives  the  results. 

The  reader's  attention  is  called  to  the  last  two  rows  of  figures 
(Table  XXXVI)  giving  the  difference  between  the  observed  and 
the  calculated  osmotic  pressures,  since  if  this  difference  actually 
represents  the  osmotic  pressure  due  to  the  gelatin  particles,  the 
figures  should  be  in  direct  proportion  to  the  concentration  of  the 
gelatin.  The  experiments  were  all  made  in  duplicate  to  give 
some  idea  of  the  magnitude  of  error,  and  it  is  obvious  that  the 
error  may  be  considerable,  25  per  cent  or  more,  because  the 
errors  in  the  observed  and  the  calculated  values  are  additive. 
Thus  the  " difference"  is  for  0.75  per  cent  solution  in  one  case  92, 
in  the  other  61,  a  variation  of  50  per  cent!  If  we  take  this  into 
consideration  we  may  conclude  that  the  differences  between 
the  observed  and  the  calculated  osmotic  pressures  are  compatible 
with  the  idea  that  the  difference  is  the  value  for  the  osmotic 
pressure  due  to  the  gelatin  particles  in  solution. 

This  would  lead  us  to  the  conclusion  that  the  osmotic  pressure 
due  to  the  gelatin  particles  in  a  1  per  cent  solution  (of  originally 
isoelectric  gelatin)  of  gelatin  phosphate  of  pH  3.60  is  about  100 
mm.  H2O.  Since  the  osmotic  pressure  of  one  grammolecule  is 
about  250,000  mm.  H2O  and  since  1  liter  of  a  1  per  cent  solution 
of  gelatin  contains  10  gm.  of  gelatin,  the  molecular  weight  of 
gelatin  should  be  expected  to  be  in  the  neighborhood  of  25,000. 


186 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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187 


The  experiment  just  described  for  gelatin  phosphate  was  repeated 
for  gelatin  chloride,  with  similar  results. 

According  to  DakhYs1  recent  analyses  gelatin  contains  1.4 
per  cent  phenylalanine.  Since  one  molecule  of  gelatin  cannot 
contain  less  than  one  molecule  of  phenylalanine  and  since  the 
molecular  weight  of  this  amino-acid  is  165  the  lowest  possible 
weight  of  gelatin  is  11,800.  If  a  molecule  of  gelatin  contains 
two  molecules  of  phenylalanine,  the  molecular  weight  should  be 
about  23,600.  This  would  be  approximately  the  figure  we  might 
expect  from  the  data  of  Table  XXXVI  on  the  assumption  that 
the  differences  in  the  last  two  rows  may  be  considered  to  be  the 
values  of  the  osmotic  pressure  of  the  protein  particles. 

TABLE  XXXVII. — INFLUENCE  OF  CONCENTRATION  OF  ALBUMIN  CHLORIDE 
OF  pH  OF  ABOUT  3.4  on  THE  OSMOTIC  PRESSURE 


Concentration  of  egg  albumin  in  per  cent 

4 

3 

2 

1 

X 

K 

pH  inside  at  equilibrium  
pH  outside  at  equilibrium  

3.34 
2.98 

45.7 
104.7 
194.0 

76.0 

3.32 
2.97 

47.9 
107.2 
192.0 

74.0 

3.38 
3.07 

41.7 
85.1 
132.0 

45.0 

3.40 
3.14 

39.8 
72.4 
92.0 

27.0 

3.40 
3.19 

39.8 
64.5 
64.6 

15.0 

3.40 
3.24 

39.8 
57.5 
43.3 

8.0 

y  —  CH  inside  X  10* 

*  —  CH  outside  X  10s 

(x  +  y)(x  -  y)  

z  =  

y 

2y  +  z  —  2x 

Observed  osmotic  pressure   

776.0 
190.0 
586.0 

555.0  + 
185.0 
370.0  + 

375.0 
113.0 

262.0 

163.0 
67.0 
96.0 

75.0 
39.0 
36.0 

36.0 
20.0 
16.0 

Calculated    osmotic    pressure    (ignoring    al- 
bumin)   

Difference  (osmotic  pressure  due  to  albumin) 

A  similar  experiment  was  made  with  different  concentrations  of 
solutions  of  the  chloride  of  crystalline  egg  albumin.  The  original 
pH  of  the  albumin  chloride  solution  was  3.5  and  that  of  the  outside 
solution  3.0.  After  equilibrium  was  established  the  pH  both 
inside  and  outside  was  slightly  changed  as  is  shown  in  Table 
XXXVII.  The  osmotic  pressures  for  0.25  to  4  per  cent  solutions 

1  DAKIN,  H.  D.,  J.  Biol.  Chem.,  vol.  44,  p.  499,  1920. 


188  THEORY  OF  COLLOIDAL  BEHAVIOR 

of  albumin  chloride  were  measured  and  calculated  for  2y  -\-  z  —  2x. 
The  difference,  which  should  be  the  osmotic  pressure  of  the  albu- 
min particles  in  solution,  is  found  in  the  last  row.  It  is  almost 
identical  with  the  difference  found  for  gelatin  chloride  for  the 
same  concentration  of  gelatin. 

We  therefore  come  to  the  conclusion  that  the  Donnan  equilib- 
rium theory  allows  us  to  explain  and  to  derive  mathematically 
the  influence  of  pH,  of  valency  of  ions,  of  concentration  of  neutral 
salt,  and  of  concentration  of  protein  on  the  osmotic  pressure; 
and  that  the  values  calculated  for  the  osmotic  pressure  on  the 
basis  of  this  theory  agree  within  the  limits  of  the  accuracy  of  the 
experiments  with  those  actually  observed,  though  the  accuracy 
of  the  experiments  is  considerably  less  than  in  the  case  of  the 
P.D.  measurements. 


CHAPTER  XI 

SWELLING 

Procter  (1914)  and  Procter  and  Wilson  (1916)  applied 
Donnan's  equilibrium  theory  to  the  explanation  of  the  swelling 
of  gelatin  in  acid.  According  to  these  authors,  the  force  which 
causes  the  entrance  of  water  and  hence  the  increase  of  volume  in 
a  solid  block  of  gelatin  in  acid  is  osmotic,  and  the  opposing  force 
which  limits  the  swelling  is  the  force  of  cohesion  between  the 
gelatin  molecules  or  ions  constituting  the  framework  inside  of 
which  the  water  is  occluded.  These  cohesive  forces  thereby  play 
the  same  role  in  the  swelling  equilibrium  as  does  the  hydrostatic 
pressure  on  the  membrane  in  the  experiments  on  osmotic  pressure. 

The  protein  ions  constituting  a  jelly  of  gelatin  chloride  cannot 
diffuse  and  hence,  according  to  Procter  and  Wilson,  can  exercise 
no  measurable  osmotic  pressure,  while  the  chlorine  anions  in 
combination  with  them  are  retained  in  the  jelly  by  the  electro- 
static attraction  of  the  gelatin  ion  but  exert  osmotic  pressure. 
This  difference  in  the  diffusibility  of  the  two  opposite  ions  of  the 
gelatin  chloride  gives  rise  to  the  condition  leading  to  the  establish- 
ment of  Donnan's  membrane  equilibrium.  It  is  immaterial 
for  this  equilibrium  whether  the  diffusion  of  dissolved  protein 
ions  is  prevented  by  a  collodion  membrane,  or  whether  it  is  pre- 
vented by  the  forces  of  cohesion  between  the  gelatin  ions  of  a 
solid  gel.  If  x  be  the  concentration  of  the  H  and  Cl  ions  in  the 
outside  solution,  y  the  concentration  of  the  free  H  and  Cl  ions  in 
the  solid  gel,  and  z  the  concentration  of  Cl  ions  in  combination 
with  gelatin,  the  Donnan  equilibrium  is  expressed  by  the  equation 

x2  =  y(y  +  z) 
and  the  osmotic  force  e  for  the  absorption  of  water  by  the  gel  is 

e  =  2y  +  z  -  2x 

The  reader  will  notice  that  this  is  the  formula  applied  later  by 
the  writer  to  osmotic  pressure. 

189 


190  THEORY  OF  COLLOIDAL  BEHAVIOR 

J.  A.  and  W.  H.  Wilson1  developed  Procter's  line  of  reasoning 
further  and  derived  the  following  formula  by  purely  mathe- 
matical reasoning  from  the  assumption  that  gelatin  combines 
chemically  with  hydrochloric  acid  to  form  a  highly  ionizable 
gelatin  chloride: 


V(K  +  y)(CV  +  2VCYy)  -  y  =  0 

where  V  is  the  increase  in  volume  in  cubic  centimeters  of  one 
milliequivalent  weight  of  gelatin,  C  is  the  constant  corresponding 
to  the  modulus  of  elasticity  of  the  gelatin,  and  K  is  a  constant 
defined  by  the  equation 

[gelatin]  [H+]  =  ^[gelatin  ion] 

Given  the  constants,  it  is  obviously  possible  to  calculate  all  the 
variables  of  the  equilibrium. 

Procter  and  Wilson  found  the  value  K  =  0.00015  by  means 
of  the  hydrogen  electrode  on  gelatin  solutions  and  the  value  C 
=  0.0003  at  18°C.  from  experiments  on  the  swelling  of  gelatin 
jellies.  From  Procter's  data  on  gelatin,  Wilson2  calculated  768 
as  its  equivalent  weight.  Using  these  constants,  Wilson  and 
Wilson  calculated  the  variables  V,  y,  and  z  for  comparison  with 
the  data  obtained  experimentally  by  Procter.  The  calculated 
and  observed  results  are  shown  in  Table  XXXVIII  and  it  will 
be  seen  that  the  agreement  is  absolute,  within  the  limits  of 
Procter's  experimental  error.  This  is  shown  even  more  strik- 
ingly when  the  values  are  plotted.  Procter  and  Wilson  regard 
this  as  establishing  their  theory  quantitatively. 

The  relation  of  V  to  e  is  governed  by  Hooke's  law,  ut  tensio 
sic  vis,  and  since  e  represents  a  pressure  equal  in  all  directions, 
the  result  is  a  pull  upon  the  jelly  equal  in  each  dimension.  The 
quantitative  expression  is 

e  =  CV 

where  the  constant  C  is  determined  by  the  bulk  modulus  of  the 
gelatin. 

1  WILSON,  J.  A.,  and  WILSON,  W.  H.,  J.  Am.  Chem.  Soc.,  vol.  40,  p.  886, 
1918. 

2  WILSON,  J.  A.,  J.  Am.  Leather  Chem.  Assn.,  vol.  12,  p.  108,  1917. 


SWELLING 
TABLE  XXXVIII1 


191 


X 

V 

y 

z 

Calculated 

Observed 

Calculated 

Observed 

Calculated 

Observed 

0.0032 

43.2 

41.2 

0.0005 

0.0005 

0.018 

0.017 

0.0073 

40.8 

44.5 

0.002 

0.002 

0.022 

0.018 

0.0077 

40.2 

40.1 

0.002 

0.002 

0.023 

0.020 

0.0120 

37.5 

39.9 

0.005 

0.006 

0.026 

0.021 

0.0122 

37.3 

39.7 

0.005 

0.006 

0.026 

0.021 

0.0170 

34.5 

31.1 

0.008 

0.009 

0.028 

0.028 

0.0172 

34.3 

37.0 

0.008 

0.009 

0.028 

0.022 

0.0406 

26.7 

28.0 

0.026 

0.030 

0.037 

0.031 

0.  0420 

26.4 

23.4 

0.027 

0.030 

0.038 

0.038 

0.0576 

24.0 

26.1 

0.041 

0.043 

0.041 

0.036 

0.  0666 

23.0 

21.4 

0.049 

0.050 

0.043 

0.045 

0.  0680 

22.8 

22.4 

0.050 

0.053 

0.044 

0.039 

0.  0930 

20.7 

17.7 

0.072 

0.072 

0.049 

0.054 

0.0944 

20.5 

20.3 

0.073 

0.072 

0.049 

0.049 

0.  1052 

19.8 

22.9 

0.083 

0.085 

0.051 

0.043 

0.1180 

18.9 

18.7 

0.095 

0.090 

0.053 

0.058 

0.  1434 

17.9 

18.4 

0.118 

0.118 

0.056 

0.055 

0.  1435 

17.9 

18.6 

0.118 

0.  118 

0.056 

0.054 

0.  1685 

17.1 

18.0 

0.141 

0.138 

0.059 

0.062 

0.  1925 

16.3 

15.8 

0.164 

0.161 

0.061 

0.068 

0.  1940 

16.2 

17.4 

0.166 

0.165 

0.061 

0.060 

0.  1945 

16.2 

17.0 

0.167 

0.164 

0.061 

0.062 

1  Observed  values  are  taken  from  PROCTER,  H.  R.,  J.  Chem.  Soc.,  vol.  105,  p.  313,  1914. 
The  observed  value  for  V  given  in  this  table  is  the  increase  in  volume  in  cubic  centimeters 
of  0.768  gm.  of  gelatin.  Values  for  x,  y,  and  z  are  given  in  moles  per  liter. 

Procter  and  Wilson  then  explain  on  the  basis  of  theDonnan 
equation  why  the  value  of  e,  and  therefore  also  V,  should  follow 
a  curve  of  the  particular  type  it  does.  By  proper  substitution 
from  the  thermodynamic  and  osmotic  equations  it  follows  that: 

e  =  -2x  +  \/4x2  +  z2 

"As  the  concentration  of  acid  is  increased  from  zero  to  some  small,  but 
finite,  value,  z  must  necessarily  increase  at  a  very  much  greater  rate  than 
x.  This  is  shown  very  markedly  in  the  most  dilute  solutions,  where 
almost  all  the  acid  added  combines  with  the  gelatin :  but  z  has  a  limiting 
value,  which  is  determined  by  the  total  concentration  of  gelatin  with 
which  we  started.  Now  z  must  either  approach  this  limiting  value  or 
diminish,  which  it  would  do  if  the  ionization  of  the  gelatin  chloride  were 
sufficiently  repressed.  In  either  case: 
limit 


192  THEORY  OF  COLLOIDAL  BEHAVIOR 

from  which  it  follows  that: 


X   =    co 

It  is  clear  from  this  that,  as  x  increases  from  zero,  e  must  increase  to  a 
maximum  and  then  decrease,  approaching  zero  asymptotically,  regard- 
less of  whether  or  not  the  ionization  of  the  gelatin  salt  is  appreciably 
repressed."1 

As  far  as  the  depressing  action  of  salt  on  swelling  is  concerned, 
Procter  and  Wilson  do  not  accept  the  idea  that  it  is  due  to  the 
repression  of  ionization. 

"  Whilst  the  salt  undoubtedly  represses  the  ionisation  of  the  gelatin 
chloride  to  some  extent,  it  would  scarcely  be  sufficient  to  account 
for  the  fact  that  salt  reduces  the  volume  of  jelly  almost  to  that  of  dry 
gelatin.  The  chief  action  is  probably  that  the  addition  of  salt  corre- 
sponds with  an  increase  in  the  value  of  #,  and  that  this  increase  in  x 
must,  according  to  the  equation  just  discussed,  produce  a  decrease  in 
the  value  of  e,  with  a  corresponding  diminution  of  the  volume  of  the 
jelly."1 

There  can  be  little  doubt  that  the  osmotic  theory  of  Procter 
and  Wilson  accounts  quantitatively  for  the  process  of  swelling; 
no  other  theory  has  thus  far  been  offered  which  can  claim  the 
same  result. 

The  force  which  opposes  and  limits  the  swelling  is  the  cohesion 
between  the  molecules  or  ions  constituting  the  gel.  When  this 
force  is  diminished  the  swelling  should  increase.  Procter  and 
Wilson  have  pointed  out  that  this  is  the  case  since  the  swelling 
of  gelatin  increases  when  the  gel  is  heated.2 

The  forces  of  cohesion  depend  not  only  on  temperature  but 
also  on  chemical  constitution.  They  are  forces  of  the  same  kind 
as  the  forces  determining  solution;  and  it  is  well  known  that,  e.g., 
the  substitution  of  Na  for  H  in  oleic  acid  increases  the  solubility 
of  the  substance  in  water,  and  that  the  substitution  of  K  for  Na 
increases  the  solubility  still  more.  We  might  a  priori  expect  that 
the  forces  of  cohesion  in  a  solid  jelly  of  gelatin  would  also  change 
considerably  with  the  nature  of  the  ion  in  combination  with 

1  PROCTER,  H.  R.,  and  WILSON,  J.  A.,  /.  Chem.  Soc.,  vol.  109,  p.  317,  1916. 

2  PROCTER,  H.  R.,  and  WILSON,  J.  A.,  J.  Chem.  Soc.,  vol.  109,  p.  315,  1916. 


SWELLING  193 

the  gelatin.  This  is,  however,  as  a  rule,  not  the  case.  Only 
the  valency  but  not  the  nature  of  the  ion  in  combination  with 
gelatin  influences  the  swelling  of  gelatin.  Thus,  at  the  same 
temperature,  at  the  same  pH,  and  the  same  concentration 
of  originally  isoelectric  gelatin,  the  swelling  of  gelatin  chloride, 
nitrate,  trichloracetate,  oxalate,  tartrate,  phosphate,  citrate, 
etc.,  is  approximately  the  same,  while  that  of  gelatin  sulphate  is 
considerably  lower.  The  swelling  of  Li,  Na,  K,  and  NH4 
gelatinate  is  also  practically  the  same  at  the  same  pH  and  the 
same  concentration  of  originally  isoelectric  gelatin,  but  the 
swelling  of  Mg,  Ca,  and  Ba  gelatinate  is  considerably  less  (see 
Chap.  V). 

It  was  shown  in  Chap.  V  that  the  same  valency  effect  which 
exists  in  regard  to  osmotic  pressure  exists  also  in  regard  to  swell- 
ing, and  the  theoretical  discussion  given  in  the  preceding 
chapter  for  this  valency  effect  in  the  case  of  osmotic  pressure 
covers  also  the  similar  effect  in  the  case  of  swelling. 

In  the  case  of  casein-acid  salts,  which  are  less  soluble  than 
gelatin-acid  salts,  the  nature  of  the  anion  is  not  without  influence 
on  the  cohesive  forces.  Thus  casein  trichloracetate  is  practically 
as  insoluble  as  casein  sulphate,  and  neither  of  the  two  salts  is 
capable  of  swelling;  while  the  more  soluble  casein  chloride  and 
casein  phosphate  are  capable  of  swelling.  In  the  latter  case  the 
valency  rule  also  holds  since  the  degree  of  swelling  is  practically 
the  same  for  casein  phosphate  and  casein  chloride,  at  the  same 
pH  temperature  and  concentration  of  originally  isoelectric 
casein.1  The  valency  rule  holds  wherever  colloidal  behavior  is 
concerned,  since  colloidal  behavior  is  only  the  consequence  of  the 
Donnan  equilibrium  and  the  equilibrium  equation  is  only  con- 
cerned with  the  sign  and  valency  of  the  ion.  The  problems  of 
solubility  and  of  cohesion  have  only  an  indirect  connection  with 
colloidal  behavior,  and  the  fact  that  solubility  and  cohesion  depend 
upon  the  specific  nature  of  the  ion  (in  addition  to  its  sign  of  charge 
and  valency)  is  not  in  conflict  with  the  other  fact  that  in  the  truly 
colloidal  phenomena  only  the  sign  of  charge  and  valency  of  an 
ion  are  concerned. 

At  the  isoelectric  point  gelatin  is  practically  not  ionized  and 
there  can  therefore  be  no  Donnan  equilibrium.  Yet  when  dry 

1  LOEB,  J.,  and  LOEB,  R,  F.,  J,  Gen.  Physiol.,  vol.  4,  p.  187,  1921-22. 
13 


194  THEORY  OF  COLLOIDAL  BEHAVIOR 

grains  of  isolectric  gelatin  are  put  into  water  of  pH  4.7,  a  consid- 
erable swelling  occurs.  The  swelling  must  be  determined  by 
forces  different  from  those  set  up  by  the  Donnan  equilibrium. 
In  the  first  place,  there  are  those  forces  of  chemical  attraction 
between  the  molecules  of  water  and  certain  of  the  groups  of  the 
gelatin  molecule  which  cause  the  solution  of  gelatin  in  water  when 
the  forces  of  cohesion  between  the  gelatin  molecules  forming  the 
gel  can  be  overcome.  The  absorption  of  water  by  dry  grains  of 
isoelectric  gelatin  at  pH  4.7  is,  therefore,  primarily  but  in  all 
probability  not  exclusively  due  to  the  residual  valency  forces,  and 
the  swelling  of  solid  isoelectric  gelatin  granules  is  primarily  a 
phenomenon  of  solid  solution. 


CHAPTER  XII 

VISCOSITY1 

1.  We  have  seen  in  Chaps.  V  and  VI  that  the  influence  of 
electrolytes  on  the  viscosity  of  the  solutions  of  certain  proteins, 
e.g.,  gelatin  or  casein,  is  similar  to  the  influence  of  electrolytes 
on  osmotic  pressure,  swelling,  and  potential  differences.  The 
explanation  given  for  the  influence  of  electrolytes  on  the  last 
named  properties  was  based  on  the  theory  of  Donnan's  membrane 
equilibirum.  This  theory  can  only  be  applied  where  the  diffusion 
of  one  type  of  ions  is  prevented,  while  no  such  block  exists  for 
other  ions.  In  the  experiments  on  osmotic  pressure  or  P.D.  of 
protein  solutions  the  collodion  membrane  permits  the  diffusion  of 
crystalloidal  ions  while  preventing  the  diffusion  of  the  protein 
ions ;  and  in  the  case  of  the  solid  gel  the  protein  ions  are  prevented 
by  the  forces  of  cohesion  from  diffusing  into  the  surrounding  solu- 
tion free  from  protein.  But  this  raises  the  problem  of  how  the 
Donnan  equilibrium  can  be  applied  to  the  viscosity  of  protein 
solutions.  We  intend  to  show  that  the  answer  lies  in  the  fact  that 
although  protein  solutions  may  be  and  probably  are  as  a  rule  true 
solutions,  consisting  of  isolated  protein  ions  and  molecules  dis- 
tributed equally  through  the  water,  they  contain  under  certain 
conditions  submicroscopic  solid  particles  of  protein.  We  shall  see 
that  the  viscosity  of  protein  solutions  is  only  influenced  in  the 
same  way  by  electrolytes  as  is  the  osmotic  pressure,  when  such 
solid  protein  particles  are  present  in  considerable  numbers.  If 
they  are  absent,  or  if  they  are  scarce,  electrolytes  will  not  influ- 
ence the  viscosity  of  protein  solutions  in  the  same  way  as  electro- 
lytes influence  the  osmotic  pressure  or  the  P.D.  of  protein  solu- 
tions. In  the  following  discussion  we  shall  measure  the  viscosity 
of  protein  solutions  by  the  time  of  outflow  through  a  capillary 
tube,  as  described  by  Ostwald,  and  the  quotient  of  this  time  over 
the  time  of  outflow  of  pure  water  through  the  same  viscometer  at 

^OEB,  J.,  J.  Gen.  Physiol.,  vol.  3,  p.  827,  1920-21;  vol.  4,  pp.  73,  97, 
1921-22.  LOEB,  J.,  and  LOEB,  R.  F.,  /.  Gen.  Physiol.,  vol.  4,  p.  187,  1921-22. 

195 


196  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  same  temperature  will  be  referred  to  as  the  relative  viscosity 
or  as  the  viscosity  ratio  of  the  protein  solution.  This  method  of 
measuring  the  relative  viscosity  will  require  improvement  but  it 
suffices  for  an  approximate  test  of  the  validity  of  the  theory. 

Einstein1  has  developed  a  theory  of  the  viscosity  of  solutions 
which  makes  the  viscosity  a  linear  function  of  the  relative  volume 
occupied  by  the  solute  in  the  solution 

7?  =  Wl  +  2.5<rf  (1) 

where  rjo  is  the  viscosity  of  the  water  at  the  temperature  of  the 
experiment,  rj  the  viscosity  of  the  solution,  and  <p  the  fraction  of 
the  volume  occupied  by  the  solute  in  the  volume  of  the  solution. 
As  Einstein  points  out,  this  formula  can  only  be  used  when  <p  is 
very  small  and  when  the  particles  of  the  solute  are  spherical  and 
large  in  comparison  with  the  molecules  of  the  solvent.  This 
condition  is  no  longer  fulfilled  in  protein  solutions  when  the 
relative  volume  occupied  by  the  protein  in  the  solution  becomes 
too  large. 

Several  authors  have  tried  to  modify  Einstein's  formula  in 
order  to  make  it  applicable  to  higher  concentrations  of  protein 
solutions.  Hatschek2  proposed  to  replace  the  constant  2.5  of 
Einstein's  formula  by  the  constant  4.5,  but  his  deductions  have 
been  criticised  both  by  Smoluchowski3  and  by  Arrhenius.4 
Arrhenius  has  shown  that  a  logarithmic  formula,  which  he  derives 
very  ingeniously  from  Einstein's  formula,  fits  the  actual  observa- 
tions in  a  satisfactory  way,  this  formula  being 

log  ri  -  log  TJO  =  <V  (2) 

where  <p  is  again  the  fraction  of  volume  occupied  by  the  protein 
in  solution,  $  a  constant,  while  rj  and  170  have  the  same  significance 
as  in  Einstein's  equation.  We  shall  make  use  of  Arrhenius's 
equation  (2)  when  we  are  dealing  with  higher  viscosities. 

Both  the  formulae  of  Einstein  and  of  Arrhenius  make  the 
viscosity  a  function  of  the  relative  volume  occupied  by  the  solute 

1  EINSTEIN,  A.,  Ann.  Physik,  vol.  19,  p.  289,  1906;  vol.  34,  p.  591,  1911. 

2  HATSCHEK,  E.,  Kolloid-Z.,  vol.  11,  p.  280,  1912. 

3  SMOLUCHOWSKI,  M.,  Kolloid-Z.,  vol.  18,  p.  190,  1916. 

4  ARRHENIUS,   S.,   Meddelanden   K.    Vetenskapsakademiens  Nobelinstitut, 
vol.  3,  No.  21,  1917. 


VISCOSITY  197 

in  the  solution,  and  it  must  be  our  task  to  correlate  the  influence 
of  electrolytes  on  viscosity  with  corresponding  variations  of  the 
volume  of  the  protein  in  solution. 

The  question  then  arises,  How  can  the  same  mass  of  protein 
particles  in  solution  change  its  relative  volume  under  the  influ- 
ence of  electrolytes?  This  is  only  possible  if  the  relative  volume 
occupied  by  the  protein  in  the  solution  is  increased  by  water 
shifting  from  solvent  to  solute.  We,  therefore,  have  to  find  out 
whether  or  not  a  shifting  of  water  from  the  solvent  to  the  solute 
is  possible,  so  that  the  volume  of  the  solvent  is  diminished  and 
that  of  the  solute  increased.  It  is  generally  assumed  that  the 
mechanism  for  such  a  transfer  of  water  from  solvent  to  solute  is 
explained  by  Pauli's  hydration  theory  which  has  been  repeatedly 
referred  to  in  this  volume.  Pauli  suggested  that  the  ionized 
molecule  of  protein  is  surrounded  by  a  shell  of  water  which  is 
lacking  in  the  non-ionized  molecule.  When  protein  is  ionized, 
i.e.,  by  the  addition  of  acid  or  alkali  to  isoelectric  protein,  a  shell 
of  water  is  formed  around  each  individual  protein  ion.  On  this 
basis  we  can  understand  why  the  viscosity  of  a  solution  of  iso- 
electric protein  should  increase  with  the  addition  of  acid  or 
alkali.  The  work  of  Lorenz,  Born,  and  others,  however,  casts  a 
doubt  on  the  assumption  of  a  general  hydration  of  polyatomic 
ions.  There  are  still  other  facts  which  show  that  the  mere 
ionization  and  consequent  hydration  of  the  individual  protein  ions 
cannot  well  be  the  cause  of  the  influence  of  the  pH  on  the  relative 
viscosity  of  gelatin  solutions. 

Gelatin  solutions  show  the  characteristic  influence  of  the  pH 
on  their  viscosity,  as  is  demonstrated  in  Fig.  48.  The  viscosity 
of  gelatin  solutions  behaves  qualitatively  as  we  might  expect  on 
the  basis  of  Pauli's  hydration  theory.  Yet,  if  hydration  of  the 
individual  protein  ions  were  the  cause  of  the  variation  of  the 
viscosity  of  gelatin  solutions,  a  variation  of  the  hydrogen  ion 
concentration  should  have  a  similar  influence  on  the  viscosity 
of  solutions  of  simple  amino-acids,  like  glycocoll  and  alanine,  to 
that  which  it  has  on  the  viscosity  of  gelatin  solutions.  Five 
per  cent  solutions  of  glycocoll  and  alanine  were  brought  to  differ- 
ent pH,  from  5.0  to  2.0  and  below,  by  the  addition  of  HC1. 
Miss  Brakeley  found,  in  the  writer's  laboratory,  that  the  variation 
of  the  pH  of  5  per  cent  solutions  of  these  two  amino-acids  between 


198 


THEORY  OF  COLLOIDAL  BEHAVIOR 


the  limits  of  5.0  and  1.16  had  no  measurable  influence  on  the 
viscosity  of  the  solution.  G.  Hedestrand1  found  in  Euler's 
laboratory  a  slight  variation  in  the  viscosity  of  2  N  glycocoll 
solutions  upon  the  addition  of  acid  or  alkali;  the  minimum  was 
found  at  pH  6.4  where  the  viscosity  was  about  1.36,  while  at 


"5   3.5 
•B    3.0 


2.5 


8 


2.0 


1.5 


1.0 


gelatin 


pH    1.4   1.6    15  2.0  2.2  2.4  26  28  3.0  3.2  3.4  3.6  3.8  40  4.2  4.4  4.6 

FIG.   48. — Influence   of  pH   on   viscosity   of  freshly  prepared   gelatin   chloride 

solutions. 

pH  3.0  it  was  1.38.  This  is  an  influence  of  pH  of  a  much  lower 
order  of  magnitude  than  the  one  found  in  the  case  of  gelatin  solu- 
tions or  casein  solutions.  These  results  cast  a  serious  doubt  on 
the  assumption  that  the  variations  in  the  curve  of  the  viscosity 
of  gelatin,  as  expressed  in  Fig.  48,  were  caused  by  variations  in 
the  hydration  of  the  individual  gelatin  ions. 

This  doubt  was  increased  by  experiments  on  the  influence  of  pH 
on  the  viscosity  of  crystalline  egg  albumin  which  indicated  only  a 
slight,  almost  negligible  influence  of  the  pH  on  the  viscosity.  Fig- 
ure 49  gives  such  an  experiment  with  3  per  cent  originally  iso- 
electric  albumin  brought  to  different  pH  through  the  addition 
of  HC1.  The  ordinates  are  the  viscosity  ratios  of  albumin  solu- 
tion over  water,  drawn  on  a  larger  scale  than  those  in  Fig.  48,  and 
the  abscissae  are  the  pH  of  the  solution.  It  is  obvious  that  if  com- 
pared with  the  gelatin  curves  the  pH  has  only  a  very  slight 

1  HEDESTRAND  G.,  Arkiv  Kemi,  Min.  och  Geol.,  vol.  8,  p.  1,  1921. 


VISCOSITY 


199 


influence  on  the  viscosity  of  solutions  of  crystalline  egg  albumin 
between  pH  4.6  and  pH  1.0.  With  a  further  lowering  of  pH  the 
viscosity  suddenly  rises,  a  fact  to  which  we  shall  return  later. 

The  method  of  the  experiments  was  as  follows:  50-c.c. samples 
of  a  6  per  cent  solution  of  isoelectric  crystalline  egg  albumin  were 
mixed  with  50  c.c.  of  HC1  solutions  of  different  concentrations 
and  the  pH  measured.  The  solutions  were  rapidly  brought  to  a 
temperature  of  24°C.  and  the  viscosity  was  measured  immediately 
at  that  temperature. 


1.5 
1.4 
13 
12 
11 
m 

• 

24' 

C. 

^, 

37o 

alb 

urn 

in  < 

:Mc 

rifl 

£. 

V 

»  — 

- 

—  — 

,*— 

•— 

—  •- 

—  » 

—  •- 

——4 

• 

-^- 

—           • 

—  •- 

—  • 

pH  0.8  1.0   .12    1.4  16    l&  2.0  23.  24  26  28  3.0  3.2  3.4  36  3.8  4.0  42  44 

FIG.  49. — Showing  that  solutions  of  crystalline  egg  albumin  have  a  low  vis- 
cosity in  comparison  with  gelatin  solutions,  and  that  the  pH  has  little  influence 
on  the  viscosity  of  solutions  of  crystalline  egg  albumin  at  pH  over  1.0  and  at 
ordinary  temperature. 

The  question  then  arises,  Why  do  amino-acids  and  at  least  one 
protein,  namely  crystalline  egg  albumin,  behave  so  differently 
from  gelatin  in  regard  to  the  influence  of  the  pH  on  the  viscosity 
of  their  solutions?  As  long  as  we  assume  that  the  influence  of 
the  hydrogen  ion  concentration  on  the  viscosity  of  gelatin-acid 
salt  solution  is  due  to  the  hydration  of  the  individual  protein 
ions  this  difference  is  incomprehensible,  since  the  amino-acids 
as  well  as  crystalline  egg  albumin  should  in  this  case  show  the 
same  influence  of  ionization  on  viscosity  as  the  gelatin. 

The  puzzle  becomes  still  greater  if  we  take  into  consideration 
the  fact  that  the  osmotic  pressure  of  solutions  of  crystalline  egg 
albumin  is  affected  in  the  same  way  by  the  hydrogen  ion  con- 
centration as  is  the  osmotic  pressure  of  gelatin  solutions  (Chap. 
V).  Why  then  do  these  two  proteins  behave  so  differently  as 
regards  the  influence  of  the  pH  on  their  viscosity? 

We  get  an  answer  to  this  question  by  comparing  the  order  of 
magnitude  of  the  viscosity  of  solutions  of  crystalline  egg  albumin 
and  of  gelatin.  The  viscosity  of  solutions  of  crystalline  egg 


200 


THEORY  OF  COLLOIDAL  BEHAVIOR 


albumin  has  a  comparatively  low  order  of  magnitude  if 
compared  with  the  viscosity  of  solutions  of  gelatin  of  the  same 
concentration  of  protein  and  the  same  pH.  The  viscosity  of 
solutions  of  crystalline  egg  albumin  of  pH  5.1,  (i.e.,  near  the 
isoelectric  point)  of  concentrations  from  1  to  14  per  cent,  was 
measured  at  15°C.  (Fig.  50).  The  viscosity  is  not  only  low  but  is 
also  practically  a  linear  function  of  the  concentration.  Figure  51 
gives  the  viscosity  of  different  concentrations  of  solutions  of 


1.0 


0.5 


Vis 

cos 

py 

of. 

SOki 

tior 

IS  C 

>f 

«& 

al 

bur 

am 

P] 

1=5 

lat 

15' 

C. 

r  — 

^~* 

>-  —  • 

__-< 

, 

1-  —  ^ 

—^ 

0     1      2     3     4     5     6      7     8     9     10    11    12    13    14 

Concentration  of  albumin   in  per  cent 

FIG.  50. — Viscosity  ratio  of  solutions  of  crystalline  egg  albumin  near  the 
isoelectric  point.  Inside  the  concentrations  used,  the  viscosity  ratio  is  nearly  a 
linear  function  of  the  concentration. 

isoelectric  gelatin  at  different  temperatures.  The  solutions 
were  prepared  from  the  same  stock  solution  of  isoelectric  gelatin 
and  were  rapidly  heated  to  45°C.  and  rapidly  cooled  to  the  desired 
temperature  and  then  the  time  of  outflow  in  an  Ostwald  visco- 
meter  was  measured.  This  was  done  to  avoid  the  increase  in 
viscosity  which  occurs  on  standing  and  which  is  especially  notice- 
able in  the  case  of  solutions  of  isoelectric  gelatin.  For  the  sake  of 
conformity  the  same  procedure  was  followed  in  the  case  of  solu- 
tions of  crystalline  egg  albumin.  It  is  obvious  that  where  the  pH 
influences  the  viscosity  in  the  same  sense  as  the  osmotic  pressure, 
e.g.,  in  the  case  of  gelatin  solutions,  the  viscosity  is  of  a  much 
higher  order  of  magnitude  than  where  the  pH  has  no  such  influ- 
ence on  viscosity  as  is  the  case  in  solutions  of  crystalline  egg 
albumin. 

It  now  remains  to  show  that  this  difference  in  the  order  of 
magnitude  of  the  viscosity  of  the  two  solutions  is  connected  with 
the  relative  volume  occupied  by  the  protein  in  solution.  The 
low  order  of  magnitude  of  the  viscosity  of  solutions  of  crystalline 


VISCOSITY 


201 


egg  albumin  suggests  a  small  relative  volume;  and  if  this  be  true 
the  viscosity  of  solutions  of  crystalline  egg  albumin  should  obey 
the  Einstein  formula;  while  the  high  order  of  magnitude  of 
viscosity  of  the  solutions  of  gelatin  suggests  that  a  larger  volume  is 


0  0.25  0.5          1.0          15         20          £5         3.0 

Concentration  of  gelatin  in  per  cent 


4.0 


FIG.  51. — Influence  of  concentration  on  the  viscosity  of  solutions  of  isoelectric 

gelatin. 

occupied  by  the  gelatin  particles  in  solution  and  hence  the  con- 
stant 2.5  of  Einstein's  formula  should  be  found  too  small;  in  other 
words,  the  Einstein  formula  should  be  replaced  by  some  other 
formula,  e.g.,  that  of  Arrhenius. 

Einstein's  formula  is  —  =  1  +  2.5<p,  where  <p  is  the  relative 

*?o 

volume  occupied  by  the  protein  in  the  solution,  and  -     is    the 


202 


THEORY  OF  COLLOIDAL  BEHAVIOR 


viscosity  ratio,  i.e.,  time  of  outflow  of  solution  over  time  of 
outflow  of  water.  The  volume  occupied  by  the  protein  in  100 
c.c.  of  solution  is 

(•n        A  100 

<p=(^~ 


2.5 


By  dividing  the  weight  of  albumin  in  solution  by  its  volume  we 
should  obtain  the  density  of  albumin.  Determinations  of  the 
density  of  albumin,  by  direct  methods,  give  the  value  of  1.36 
(Arrhenius).  Table  XXXIX  shows  that  if  we  calculate  the 


TABLE  XXXIX 


Concentration 
of  crystalline 
egg  albumin, 
per  cent 

?.-' 

Calculated 
volume  of 
albumin,  cubic 
centimeters 

Calculated 
density  of 
albumin 

14 

0.290 

11.6 

1.20 

12 

0.240 

9.6 

1.25 

10 

0.185 

7.4 

.35 

8 

0.132 

5.3 

.51 

6 

0.100 

4.0 

.50 

4 

0.074 

2.96 

.36 

2 

0.042 

1.7 

.17 

density  of  albumin  on  the  basis  of  Einstein's  formula,  we  obtain 
values  which  differ  only  inside  the  limits  of  accuracy  from  the 
value  1.36  obtained  by  direct  determination.  The  time  of 
outflow  of  water  through  the  viscometer  was  in  this  case  227 
seconds  at  15°C.  These  measurements  show  that  the  low  order 
of  magnitude  of  the  viscosity  of  solutions  of  crystalline  egg 
albumin  is  accompanied  by  a  volume  of  albumin  sufficiently  low 
to  permit  the  application  of  Einstein's  formula,  with  the  constant 
2.5. 

When  we  try  to  apply  Einstein's  formula  in  the  same  way  to 
the  viscosity  measurements  of  isoelectric  gelatin  solutions  we  find 
that  the  relative  volume  of  gelatin  in  the  solution  and  its  density 
calculated  on  the  basis  of  the  constant  2.5  lead  to  impossible 
results.  Thus  the  density  of  gelatin  is  probably  not  very  differ- 


VISCOSITY 


203 


ent  from  that  of  egg  albumin,  i.e.,  in  the  neighborhood  of  1.4. 
The  values  calculated  in  Table  XL  with  Einstein's  viscosity  con- 
stant 2.5  are  from  20  to  40  times  too  low.  Hence,  the  relative 


TABLE  XL 


Concentration 

Calculated 

Calculated 

of  isoelectric 

-  1 

volume  of 

density  of 

gelatin, 

*?o 

gelatin,  cubic 

gelatin 

per  cent 

at  35° 

centimeters 

0.5 

0.170 

6.8 

0.077 

1.0 

0.405 

16.2 

0.06 

1.5 

0.725 

29.0 

0.05 

2.0 

1.020 

40.8 

0.05 

2.5 

1.405 

56.2 

0.045 

3.0 

2.042 

81.7 

0.037 

3.5 

2.560 

102.4 

0.034 

volume  of  gelatin  in  these  solutions  is  far  beyond  the  limit  inside 
which  the  formula  of  Einstein  is  applicable.  The  formula  of 
Arrhenius  (2)  leads  to  a  fair  agreement.  According  to  this 
formula  the  logarithms  of  the  viscosity  ratio  when  plotted 
over  the  concentration  of  the  gelatin  should  give  a  straight  line. 
The  agreement  of  the  values  for  45  and  35°  with  this  theory  is 
satisfactory  (considering  the  limits  of  accuracy  of  the  measure- 
ments) the  logarithms  of  the  viscosity  increasing  practically  in 
direct  proportion  with  the  concentration  (i.e.,  the  relative 
volume)  of  the  gelatin  in  the  solution  (Table  XLI).  At  60° 
the  agreement  is  not  quite  so  good  but  still  recognizable.  At 
25°C.,  however,  it  is  satisfactory  only  at  the  lowest  concentra- 
tions, but  at  the  higher  concentrations  the  viscosity  grows  more 
rapidly  than  the  concentration.  The  reason  for  this  is,  however, 
obvious,  since  at  this  temperature  the  gelatin  solution  solidifies 
so  rapidly  that  the  viscosity  measurements  were  no  longer 
possible  for  a  concentration  of  3.5  per  cent  gelatin  solution,  and 
for  this  reason  the  value  of  the  viscosity  of  a  3  or  a  2  per  cent 
solution  is  already  too  high  on  account  of  the  mechanical  hin- 
drance of  the  flow  of  the  solution  through  the  viscometer  owing  to 
partial  solidification. 


204 


THEORY  OF  COLLOIDAL  BEHAVIOR 
TABLE  XLI 


Concentration  of 

i-_  "n 

log  — 

solution  of  iso- 

•no 

electric  gelatin, 

per  cent 

60° 

45° 

35° 

25° 

0.25 

0.0236 

0.0306 

0.0269 

0.0374 

0.5 

0.0504 

0.0682 

0.0682 

0.0792 

1.0 

0.0930 

0.1350 

0.1475 

0.1685 

1.5 

0.1656 

0.2135 

0.2367 

0.2765 

2.0 

0.2350 

0.2796 

0.3057 

0.3701 

2.5 

0.2953 

0.3512 

0.3811 

0.4691 

3.0 

0.3094 

0.4409 

0.4832 

0.6941 

3.5 

0.4321 

0.5051 

0.5514            solidifies 

4.0 

0.5214 

0.5660 

0.6043 

These  experiments  lead  to  the  following  two  conclusions. 

(a)  Since  the  viscosity  measurements  of  solutions  of  crystalline 
egg  albumin  and  of  gelatin  agree  fairly  well  with  Einstein's  and 
Arrhenius's  formula  respectively,  it  seems  that  the  viscosity  of 
the  solutions  of  proteins  is  primarily  a  function  of  the  relative 
volume  occupied  by  the  protein  in  solution. 

(6)  Since  the  measurements  were  made  at  (or  near)  the  iso- 
electric  point  of  the  two  proteins  the  difference  in  the  viscosity 
of  solutions  of  gelatin  and  of  crystalline  egg  albumin  cannot  be 
ascribed  to  differences  in  the  degree  of  hydration  of  the  individual 
protein  ions,  since  at  the  isoelectric  point  the  protein  is  not 
ionized. 

It  follows  from  these  results,  that  the  difference  in  the  order 
of  magnitude  of  the  viscosity  of  the  two  proteins  must  be  due  to 
the  fact  that  gelatin  possesses  a  mechanism  for  increasing  its 
relative  volume  in  solution  which  is  lacking  in  the  case  of  egg 
albumin  (in  not  too  high  a  concentration,  at  not  too  high  a  tem- 
perature a*nd  a  pH  above  1.0),  and  this  mechanism  seems  to  be 
connected,  in  the  case  of  gelatin  solutions,  with  their  tendency 
to  set  to  a  gel. 

Zsigmondy  (p.  98)  states  that  Smoluchowski  has  explained 
the  increase  in  the  viscosity  of  a  solution  of  aluminium  oxide 
upon  coagulation  by  the  assumption  of  an  occlusion  of  liquid 
between  the  particles.  Smoluchowski  calculates  from  the 


VISCOSITY  205 

increase  of  viscosity  during  coagulation  of  aluminium  oxide  that 
the  coagulating  particles  occupy  a  volume  400  to  500  times  as 
great  as  that  occupied  by  the  dry  material  itself.1  This  apparent 
increase  of  volume  he  explains  through  the  aggregation  of  needle- 
shaped  particles,  water  being  occluded  between  these  particles. 
Smoluchowski  apparently  did  not  associate  this  occlusion  of 
water  with  the  Donnan  equilibrium. 

If  we  adopt  this  idea  for  the  explanation  of  the  high  order  of 
viscosity  of  gelatin  solutions  as  compared  with  solutions  of  egg 
albumin  we  reach,  the  conclusion  that  the  gelatin  solutions  contain 
submicroscopic  particles  of  solid  jelly  ,  i.e.,  micellae  which  occlude 
relatively  large  quantities  of  water,  whereby  the  relative  volume 
occupied  by  the  gelatin  in  solution  is  increased,  and  that  such  par- 
ticles are  lacking  or  scarce  in  the  case  of  solutions  of  egg  albumin. 
These  particles  of  solid  jelly  are  the  precursors  of  the  continuous 
jelly  to  which  the  gelatin  solution  has  a  tendency  to  set.  The  fact 
that  these  particles  are  lacking  or  scarce  in  the  case  of  solutions  of 
egg  albumin  is  connected  with  the  fact  that  the  latter  solutions 
have  no  tendency  to  set  to  a  jelly  at  ordinary  temperature  and  a 
pH  above  1.0.  When  the  pH  is  below  1.0  and  the  temperature 
higher  the  solutions  of  crystalline  egg  albumin  set  to  a  jelly  and 
in  that  case  their  viscosity  becomes  of  the  same  high  order  of 
magnitude  as  that  of  gelatin  solutions. 

This  assumption  would  also  explain  why  the  pH  causes  a 
similar  variation  in  the  viscosity  of  gelatin  solutions  as  in  their 
osmotic  pressure,  while  the  viscosity  of  solutions  of  crystalline 
egg  albumin  shows  no  such  influence  of  the  pH.  There  must 
arise  a  Donnan  equilibrium  between  these  submicroscopic 
particles  of  solid  jelly  and  the  surrounding  solution,  and  this 
Donnan  equilibrium  must  regulate  the  amount  of  water  occluded 
by  the  submicroscopic  particles  of  solid  jelly,  floating  in  the 
gelatin  solution.  Since  the  low  order  of  magnitude  of  the  vis- 
cosity of  albumin  solutions  excludes  the  existence  of  a  consider- 
able number  of  such  submicroscopic  solid  particles  in  the  solution, 
it  becomes  obvious  that  the  Donnan  equilibrium  cannot  manifest 
itself  to  any  large  extent  in  the  viscosity  of  solutions  of  this 

1  Quoted  from  ZSIGMONDY.  The  paper  of  SMOLUCHOWSKI  is  inaccessible 
to  the  writer  since  the  number  of  the  journal  in  which  it  appeared  failed 
to  reach  the  Institute  during  and  since  the  war. 


206  THEORY  OF  COLLOIDAL  BEHAVIOR 

protein  at  not  too  high  a  concentration,  at  low  temperatures,  and 
at  pH  above  1.0. 

2.  If  this  assumption  is  correct,  it  would  follow  that  a  suspen- 
sion of  powdered  gelatin  in  water  should  have  a  greater  viscosity 
at  a  given  temperature  than  if  the  same  mass  of  gelatin  is  dis- 
solved in  water,  since  in  the  latter  case  part  of  the  gelatin  at 
least  is  in  true  solution  (as  we  shall  see  later)  and  this  latter  is 
incapable  of  increasing  its  volume  by  occluding  water.  It  would 
follow,  furthermore,  that  the  influence  of  electrolytes  on  the 
viscosity  of  suspensions  of  powdered  gelatin  would  be  the  same 
as  the  influence  of  electrolytes  on  the  osmotic  pressure  of  gelatin 
solutions.  It  can  be  shown  that  both  expectations  are  fulfilled. 

Doses  of  0.5  gm.  of  powdered  gelatin  were  put  into  100  c.c.  of 
water  containing  0,  1,  2,  3,  4,  5,  6,  7,  8,  10,  12.5,  15  and  20  c.c.  of 
0.1  N  HC1  to  bring  the  gelatin  to  different  pH.  The  suspensions 
were  allowed  to  stand  1  hour  at  20°  to  bring  about  the  swelling 
of  the  particles,  and  the  viscosity  of  the  suspensions  was  measured 
in  a  straight  viscometer  at  20°C.  The  time  of  outflow  of  water 
through  the  viscometer  at  20°  was  48.5  seconds.  The  upper 
curve  in  Fig.  52  gives  the  ratio  of  viscosity  of  suspensions  to 
that  of  water  at  20°C.  (When  the  viscosity  is  high,  the  values 
obtained  are  a  little  too  great  owing  to  a  gravity  effect  which 
causes  the  solid  particles  to  collect  above  the  upper  opening  of 
the  capillary  tube  during  a  part  of  the  time  of  the  experiment 
thus  increasing  temporarily  the  density  of  the  suspension.) 
After  the  viscosity  of  a  suspension  was  measured  the  suspension 
was  transformed  into  a  solution  by  heating  the  suspension  to  45°C. 
for  10  minutes;  after  that  the  solution  was  rapidly  cooled  to  20°C. 
and  the  viscosity  of  the  gelatin  solution  was  immediately  meas- 
ured with  the  same  viscometer  at  20°C.  The  lower  curve  in 
Fig.  52  shows  that  the  viscosity  was  now  considerably  diminished. 
The  abscissae  are  the  pH  of  the  gelatin  solutions. 

If  we  measure  the  volume  of  the  suspended  particles  we  find 
that  it  varies  in  a  similar  way  as  the  viscosity.  Samples  of  0.5 
gm.  of  Cooper's  powdered  commercial  gelatin  of  a  pH  of  about  6.0 
were  added  to  100-c.c.  portions  of  water  containing  varying 
amounts  of  HC1.  The  particles  had  uniform  size  (going  through 
sieve  100  but  not  through  sieve  120),  but  their  shape  was  ex- 
tremely irregular.  They  were  left  in  the  solution  several  hours 


VISCOSITY 


207 


at  20°C.,  and  then  their  time  of  outflow  through  a  capillary 
tube  was  ascertained  at  20°C.  The  time  of  outflow  of  water 
through  the  viscometer  at  this  temperature  was  24  seconds.  It 
was  essential  to  stir  the  suspension  thoroughly  before  sucking  it 
into  the  viscometer  since  the  gelatin  particles  sink  rapidly  to  the 
bottom  of  the  dish. 


4.0 


3.5 


3.0 
fi 


J>   2.0 

1.5 
1.0 


lulion 


Vis 


OS 


itv 


\ 


at  2 


o°c. 


pH  1.6  1.8  2.0  2.2  2.4  2.6  2.8  3.0  3.2  3.4  3.6  3.8  40  42 

FIG.  52. — Difference  in  the  viscosity  of  a  suspension  of  0.5  gm.  of  powdered 
gelatin  in  100  c.c.  and  of  the  solution  of  the  suspension  in  the  same  liquid;  both 
viscosities  were  measured  at  20°C. 

After  the  viscosity  measurements  were  taken,  the  suspension 
was  put  on  a  filter  of  cotton  wool  and  the  supernatant  water 
allowed  to  drain  off.  By  measuring  the  volume  of  the  filtrate 
and  deducting  this  from  the  original  volume  of  the  suspension 
(which  was  in  all  cases  100  c.c.),  the  volume  of  the  gelatin  was  ob- 
tained (with  a  considerable  error).  Then  the  gelatin  was  melted 
and  the  pH  of  the  melted  mass  of  gelatin  as  well  as  of  the  filtrate 
was  determined  potentiometrically.  Figure  53  gives  the  result 
of  such  an  experiment.  The  lower  curve  shows  the  influence  of 


208 


THEORY  OF  COLLOIDAL  BEHAVIOR 


the  pH  (of  the  gelatin)  on  the  viscosity,  and  the  upper  curve  the 
influence  of  the  pH  on  the  volume  of  the  gelatin.  The  two  curves 
are  similar. 

The  valency  of  the  anion  of  the  acid  influences  the  viscosity  of 
suspensions  of  protein  in  a  similar  way  as  it  does  the  viscosity 
of  solutions.  This  proof  is  furnished  in  Fig.  54.  Doses  of  0.5 
gm.  of  finely  powdered  gelatin  (going  through  a  sieve  of  mesh 


3.0 


2.5 


2.0 


1.5 


1.0 


O.I 

& 

LpC 

we 

er<= 

d 

^ 

^S 

tele 

tin 

in 

X 

«>s 

/ 

\ 

iLLS 

pei: 

£101 

I 

<$ 

^ 

^o 

o 

\ 

/> 

^ 

^ 

»  — 

>>v 

\ 

0 

s 

'. 

•( 

•^ 

V 

V 

\. 

/ 

/] 

% 

\ 

• 

\ 

t 
\ 

* 

•$ 

X 

s 

X 

^ 

L 

25 


20 


"I 

.* 


pH  1.8   2JO    22   2.4   26   Z8  ao  a2    3.4  a6   a8   40  42  4.4 

FIG.  53. — Showing  that  the  influence  of  pH  on  viscosity  of  0.5  per  cent  sus- 
pensions of  powdered  gelatin  in  water  is  similar  to  the  influence  of  pH  on  vis- 
cosity of  gelatin  solutions,  and  that  the  volume  occupied  by  the  particles  in  the 
suspension  varies  in  a  similar  way  as  the  viscosity.  Temperature  20°C. 

size  100  but  not  through  sieve  of  mesh  size  120)  of  pH  7.0  were  put 
into  a  series  of  beakers  containing  each  100  c.c.  of  HC1  of  different 
pH  and  kept  in  the  solution  over  night  at  a  temperature  of  20°C. 
Simultaneously  a  similar  series  of  beakers  containing  each  100  c.c. 
of  H3PO4  and  H2SO4  of  different  pH  (instead  of  HO)  were  pre- 
pared, each  receiving  also  0.5  gm.  of  powdered  gelatin.  After 
19  hours  the  viscosities  of  all  these  series  of  suspensions  were 
determined  at  20°C.  Figure  54  gives  the  result,  the  ordinates 
being  the  values  for  the  viscosity  ratios,  gelatin  suspension: 
water,  and  the  abscissae  are  the  pH  of  the  gelatin  particles 
at  equilibrium.  The  curves  show  that  the  viscosity  of  suspen- 
sions of  gelatin  sulphate  is  a  little  less  than  half  that  of  suspensions 
of  gelatin  chloride  and  phosphate  of  the  same  pH.  The  curves 
for  the  suspensions  of  gelatin  chloride  and  gelatin  phosphate  are 
alike,  with  the  exception  of  part  of  the  descending  branch. 


VISCOSITY 


209 


Experiments  on  the  influence  of  these  three  acids  on  swelling 
(Fig.  19,  Chap.  V)  show  that  the  curves  for  the  relative  volume  of 
powdered  gelatin  in  solutions  of  these  three  acids  are  similar  to  the 
viscosity  curves  in  Fig.  54  since  the  relative  volume  of  gelatin 
sulphate  was  found  to  be  not  far  from  one-half  of  that  of  gelatin 
chloride  or  gelatin  phosphate  of  the  same  pH. 


4.5 


4.0 


3.5 


2.5 


2.0 


1.5 


1.0 


*.u 


7 


Viscosity  of  suspen- 
sions of  05  gm.  of 
powdered  gelatin  in 
100  cc.  of  acid  solution 


\ 


pH  16   16  2.0  2.2  2.4  2.6  2.8  3.0  3.2  3.4  3.6  3.8  4.0  4.2  44  46 

FIG.  54. — Viscosity  of  suspensions  of  0.5  gm.  of  powdered  gelatin  of  grain 
size  100  to  120.  Abscissae  are  the  pH,  the  ordinates  the  ratio  of  time  of  outflow 
of  suspension  to  time  of  outflow  of  water.  The  influence  of  HC1  and  HsPC^  is 
practically  identical  for  the  same  pH  while  H2SO4  depresses  the  viscosity  of  the 
suspensions  to  a  little  less  than  one-half  of  that  for  HC1. 

We  have  seen  that  the  viscosity  of  a  gelatin  chloride  solution, 
e.g.,  of  pH  3.0,  is  lowered  when  neutral  salts  are  added  and  the  pH 
kept  constant  (Fig.  29,  Chap.  VI).  The  same  is  true  for  the 
viscosity  of  suspensions  of  powdered  gelatin.  Doses  of  0.5 
gm.  of  powdered  gelatin  of  pH  6.0,  going  through  sieve  100  but 
not  through  sieve  120,  were  put  each  into  100  c.c.  of  water  con- 
taining 6  c.c.  of  0.1  N  HC1,  and  different  quantities  of  NaNO3,  so 
that  the  concentration  of  the  salt  varied  in  the  different  solutions 
from  M/8  to  M/2,048.  One  solution  contained  no  salt.  The 

14 


210 


THEORY  OF  COLLOIDAL  BEHAVIOR 


pH  of  the  gelatin  varied  in  the  neighborhood  of  3.0;  the.  tempera- 
ture was  20°C.  After  2J£  hours,  when  the  Donnan  equilibrium 
between  the  particles  and  the  surrounding  solution  was  supposed 
to  be  established,  the  viscosity  of  each  suspension  was  measured 
at  20°C.  and  the  volume  occupied  by  the  suspended  particles  of 
gelatin  was  ascertained  in  the  manner  described.  It  was  found 


3.5 
o    3.0 

! 

£»M 
1 

!fl    2.0 
1.5 
1  n 

O.J 

>  gn 

i.p< 

wd 

er€ 

d 

25 
20 
15 
10 
5 
n 

i 

^__   < 

g< 

slat 

In  ( 

:hK 

)ric 

Le 

^ 

^s< 

1 

n  i 

(IS 

pei 

li>iU 

Ll    • 

X 

^ 

- 

i 
\ 

( 

S 

i 

\ 

i 

\ 

< 

— 

•«^^>. 

& 

> 

1 

C 

^ 

s 

s, 

S 

s 

r^ 

S 
Id 


0  2048  1024  512  256  128   64    32    16 

Concentration  ofNaN03 

FIG.  55. — Showing  depressing  influence  of  neutral  salts  on  viscosity  of  sus- 
pensions of  powdered  gelatin  in  water  and  on  the  volume  occupied  by  the  gelatin 
particles  in  the  suspension. 

that  the  addition  of  salt  diminished  the  relative  volume  of  the 
gelatin  particles  and  the  viscosity  (Fig.  55) .  Where  the  volume 
of  the  gelatin  was  great  it  no  longer  varied  parallel  with  the 
viscosity,  as  was  to  be  expected  from  the  fact  that  Einstein's 
formula  no  longer  holds  in  this  case. 

The  measurements  of  the  pH  of  the  gelatin  solution  and  the 
outside  solution  showed  that  the  addition  of  salt  diminished  the 
difference  between  the  two,  as  Donnan's  theory  demands  (Table 
XLII). 


VISCOSITY 
TABLE  XLII 


211 


Concentration  of  NaNOs 

0 

oo 
o 

<N~ 

s 

T-H 

s 

<N 

»0 

s 

s 

<N 

5" 

00 
<N 

S, 

1 

<N 

^ 

CO 
rH 

S 

pH  of  gelatin  particles  
pH  of  supernatant  liquid  .... 

3.04 
2.74 

3.04 
2.76 

3.03 
2.76 

3.02 
2.76 

3.00 

2.77 

3.02 
2.80 

2.97 

2.78 

2.94 

2.77 

2.85 
2.70 

Difference,  pH  inside  minus 
r)H  outside  

0.30 

0.28 

0.27 

0.26 

0.23 

0.22 

0.19 

0.17 

0.15 

This  demonstration  completes  the  proof  that  the  viscosity  of 
suspensions  of  powdered  gelatin  in  water  of  different  pH  is 
influenced  in  the  same  way  by  electrolytes  as  is  the  viscosity  of 
solutions  of  the  same  gelatin  salts,  and  that  this  influence  is  due, 
in  the  case  of  suspensions,  to  the  influence  of  the  Donnan  equilib- 
rium upon  the  swelling  of  the  particles. 

The  volume  V  of  gelatin  occupied  in  100  c.c.  of  the  suspension 
was  determined  by  filtering  and  deducting  the  volume  of  the 
filtrate  from  the  total  volume  of  the  suspension.  Knowing 
the  viscosity  we  can  calculate  Einstein's  constant  c  according  to 
the  formula 


..  -  c 

l     V 


c  should  be  2.5  if  V  is  sufficiently  small. 

TABLE  XLIII 


V, 
cubic  centimeters 

.2. 

1/0 

c 

12.0 

1.292 

2.5 

17.0 

1.480 

2.8 

18.0 

1.792 

4.4 

20.5 

2.064 

5.1 

20.5 

2.020 

4.9 

20.0 

1.855 

4.2 

18.0 

1.625 

3.5 

16.5 

1.542 

3.3 

212  THEORY  OF  COLLOIDAL  BEHAVIOR 

The  values  in  Table  XLIII  show  that  Einstein's  formula  gives 
the  correct  values  for  viscosity  when  the  volume  of  the  gelatin 
is  small,  since  in  that  case  c  is  equal  or  nearly  equal  to  2.5,  as  his 
formula  demands. 

When,  however,  the  volume  is  larger,  the  value  for  c  exceeds 
2.5.  The  fact  that  the  value  for  c  exceeds  2.5  when  the  relative 
volume  occupied  by  the  particles  in  the  solution  is  large,  was 
found  also  by  Hatschek,  Smoluchowski,  and  Arrhenius.  Hat- 
schek  replaced  the  value  2.5  in  Einstein's  formula  by  a  larger  one, 
namely  4.5.  This,  however,  meets  in  our  case  with  the  difficulty 
that  the  value  c  shows  a  drift  reaching  a  maximum  when  the 
volume  of  the  gelatin  particles  is  a  maximum.  This  difficulty 
is  largely  avoided  in  Arrhenius's  formula  and  we  have  to  change 
from  Einstein's  formula  to  that  of  Arrhenius  whenever  the 
relative  volume  of  the  particles  in  solution  or  suspension  exceeds 
the  limits  of  the  applicability  of  Einstein's  formula,  as  we  shall 
see  in  the  next  chapter. 

The  experiments  on  the  viscosity  of  suspensions  of  powdered 
gelatin  in  water  have,  therefore,  led  to  the  result,  first,  that  the 
influence  of  pH,  of  the  valency  of  ions,  and  of  the  concentration 
of  neutral  salts  on  the  viscosity  of  suspensions  of  finely  powdered 
gelatin  in  water  is  similar  to  the  influence  of  these  three  agencies 
on  the  viscosity  of  gelatin  solutions;  second,  that  the  influence  of 
electrolytes  on  the  viscosity  of  the  suspensions  is  due  to  the 
variation  of  the  swelling  (or  relative  volume)  of  the  suspended 
particles;  and  third,  that  this  latter  fact  explains  why  the  Donnan 
equilibrium  determines  also  the  variation  of  viscosity  of  these 
suspensions.  If  it  could  be  shown  that  a  solution  of  gelatin 
contains  also  some  (submicroscopic)  particles  of  solid  jelly 
(capable  of  swelling),  we  should  understand  at  once  why  electro- 
lytes influence  the  viscosity  of  gelatin  solutions  as  they  influence 
the  swelling,  osmotic  pressure,  or  the  P.D.  of  these  solutions. 

3.  We  have  only  indirect  means  of  testing  the  occlusion  theory 
for  gelatin  solutions  but  these  tests  give  an  unequivocal  answer. 
When  a  0.5  per  cent  solution  of  isoelectric  gelatin  is  heated  rapidly 
to  45°,  cooled  rapidly  to  a  lower  temperature,  e.g.,  20°C.,  and 
kept  at  this  temperature,  the  solution  will  ultimately  set  to  a 
continuous  gel  but  will  steadily  increase  its  viscosity  before  this 
stage  is  reached.  It  is  natural  to  assume  that  the  formation 


VISCOSITY 


213 


of  a  continuous  jelly  is  preceded  by  the  formation  of  submicro- 
scopic  pieces  of  jelly,  which  increase  in  number  and  size,  forming 
finally  a  continuous  jelly.  Hence,  the  longer  a  solution  of 
isoelectric  gelatin  stands  at  20°C.  the  greater  the  number  of 
submicroscopic  solid  pieces  of  jelly  formed  in  the  solution.  The 
submicroscopic  pieces  of  jelly,  surrounded  by  a  true  solution  of 


pHl.6   18  2.0   22  24  2.6  25  3.0  3.2  3.4  3.6  3.8  40  42  44 

FIG.  56. — Increase  in  viscosity  when  acid  is  added  to  solutions  of  isoelectric  gela- 
tin after  they  had  been  standing  for  3  and  17  hours  respectively. 

isolated  molecules  of  gelatin  in  water,  are  compelled  to  regulate 
the  amount  of  water  they  occlude  by  the  Donnan  equilibrium. 
Hence,  when  we  add  some  HC1  to  a  0.5  per  cent  solution  of  iso- 
electric gelatin  after  the  solution  has  been  standing  for  some 
hours  at  20°  we  should  expect  to  find  a  higher  viscosity  than  when 
we  add  the  same  amount  of  acid  to  the  gelatin  solution  immedi- 
ately after  it  has  been  rapidly  heated  to  45°  and  rapidly  cooled 
to  20°C. 

This  experiment  turns  out  as  expected,  as  is  shown  in  Fig.  56. 


214  THEORY  OF  COLLOIDAL  BEHAVIOR 

When  a  0.5  per  cent  solution  of  isoelectric  gelatin  is  rapidly 
heated  to  45°C.,  cooled  rapidly  to  20°C.,  and  brought  immediately 
to  a  different  pH  by  the  addition  of  HC1,  at  20°C.  a  viscosity 
curve  like  the  lowest  in  Fig.  56  is  obtained.  When,  however, 
the  0.5  per  cent  isoelectric  gelatin  solution  is  allowed  to  stand  for 
3  hours  at  20°C.  before  the  acid  is  added,  a  parallel  viscosity  curve 
is  formed  at  20°C.  but  higher  than  the  first  one  (middle  curve, 
Fig.  56),  for  the  reason  that  during  the  3  hours  an  additional 
number  of  solid  jelly  particles  capable  of  swelling  has  beenformed. 
If  the  solution  of  isoelectric  gelatin  stands  for  17  hours  at  20°C., 
before  the  HC1  is  added,  the  curve  is  still  higher  though  practically 
parallel  with  the  first  curve  (upper  curve,  Fig.  56),  except  at  the 
summit.  It  is  probable  that  on  standing  not  only  the  number 
but  the  size  of  individual  particles  also  increases,  and  the  writer 
has  observed  that  for  the  size  of  granules  used  in  his  experiments 
the  greater  the  size  the  greater  the  viscosity,  since  the  viscosity 
is  chiefly  but  not  exclusively  a  function  of  the  relative  volume  of 
the  particles. 

Since  jelly  formation  of  gelatin  is  a  reversible  process  we  should 
expect  that  two  opposite  processes  always  take  place  simultane- 
ously in  a  gelatin  solution  on  standing,  namely,  first,  the  forma- 
tion of  solid  particles  of  jelly  through  the  aggregation  of  previously 
isolated  gelatin  molecules  and  ions,  and  second,  the  dissolution 
of  such  aggregates  (micellae)  back  into  isolated  molecules  and 
ions.  It  is  easy  to  show  that  powdered  gelatin  of  a  given  pH 
dissolves  the  more  rapidly  the  higher  the  temperature.  If, 
therefore,  our  assumption  is  correct  that  in  a  solution  of  gelatin 
two  opposite  processes  go  on  constantly,  the  rate  of  melting  of 
the  micellae  should  increase  if  the  temperature  rises.  Hence, 
at  very  low  temperature  the  viscosity  of  a  gelatin  solution  should 
increase  rapidly  on  standing  since  the  formation  of  new  micellae 
takes  place  constantly,  while  practically  no  melting  of  micellae 
occurs.  When,  however,  the  temperature  is  raised  beyond  a 
certain  point,  the  rate  of  melting  of  micellae  increases  more 
rapidly  than  the  rate  of  formation  of  new  micellae.  Hence,  at 
such  a  temperature  the  viscosity  of  a  gelatin  solution  should  not 
increase  but  decrease  on  standing. 

This  conclusion  was  tested  experimentally  and  found  to  be 
correct.  A  2  per  cent  solution  of  gelatin  chloride  of  pH  2.7  was 


VISCOSITY 


215 


rapidly  heated  to  a  temperature  of  45°  and  then  rapidly  brought 
to  the  temperature  at  which  the  change  of  viscosity  of  the  solution 
with  time  was  to  be  observed.  At  definite  intervals  the  viscosity 
of  the  solution  was  measured.  Figure  57  gives  the  result.  At 


11.0 
10.0 
9.0 
8.0 


to 


'53  6.0 

I 

*>   5.0 


4.0 

ao 

2.0 


OS 


tv 


chloride 


of 


oluLiorso 


5     10    15   20   25  30   35  40  45  50  55  60 

Time  in  minutes 


FIG.  57. — Influence  of  temperature  on  the  variation  of  viscosity  of  gelatin 
solutions  on  standing.  Below  35°C.  the  viscosity  of  a  2  per  cent  gelatin  chloride 
solution  of  pH  2.7  no  longer  increases  but  diminishes  on  standing. 

15°  the  viscosity  increased  rapidly  on  standing;  at  25°  it  increased 
on  standing  but  less  rapidly;  at  35°  or  above  it  diminished  on 
standing,  the  more  rapidly  the  higher  the  temperature.  The 


216 


THEORY  OF  COLLOIDAL  BEHAVIOR 


temperature  at  which  the  two  opposite  processes — the  formation 
and  the  melting  of  micellae — occur  equally  rapidly  in  a  2  per  cent 
solution  of  gelatin  chloride  of  pH  2.7  lies  between  25  and  35°C. 


2.0 


5  10  15  20  25  30  35  40  45  50  55  60 

Time  in  minutes 

FIG.  58. — Increase  of  viscosity  of  gelatin  sulphate  solution  of  different  pH  on 
standing.  The  increase  is  most  rapid  at  the  isoclectric  point,  thus  proving  that 
the  acid  retards  or  prevents  the  formation  of  submicroscopic  solid  particles  of 
jelly  on  standing. 


When  acid  is  added  to  powdered  isoelectric  gelatin  the  time 
required  to  dissolve  the  particles  diminishes  at  a  given  tempera- 
ture with  increasing  hydrogen  ion  concentration  of  the  solution  and 
this  tendency  of  the  particles  to  dissolve  with  increasing  hydrogen 


VISCOSITY 


217 


ion  concentration  shows  no  maximum  as  does  the  swelling.     Hence 
we  should  expect  that  the  more  acid  is  added  to  a  0.5  per  cent 


CQ 

o 
o 

CO 


3.3 
3.2 
3.1 
3.0 
2.9 
2.8 
27 
2.6 
2.5 
2.4 
2.3 
2.2 
2.1 
2.0 
1.9 
1.8 
1.7 
1.6 
1.5 
1.4 


FIG.  59.- 
an  increase 
at  20°C. 


1   I   I L 


J L 


Influence  ^ 

the  rise  in  viscosity  of 
1%  gelatin  chloride 
solution  of  pH  3.4  on 
standing  at  20  °  C. 


0  5  10  15  20  25  30  35  40  45  50  55  60 

Time  in  minutes 

-Showing   that   concentrations  of  Na2SO4  of  M/32  and  above  cause 
in  the  viscosity  of  gelatin  chloride  solution  of  pH  3.4  on  standing 


solution  of  isoelectric  gelatin  the  less  the  viscosity  will  increase 
on  standing  at  a  given  temperature,  e.g.,  20°C.,  since  the  more 
acid  is  added  to  isoelectric  gelatin  the  greater  the  tendency  of 


218  THEORY  OF  COLLOIDAL  BEHAVIOR 

the  solid  jelly  particles  already  existing  to  dissolve;  while  the 
tendency  of  the  isolated  gelatin  molecules  or  ions  to  adhere  to 
each  other  is  not  increased.  It  should  follow  that  on  standing  the 
viscosity  of  a  0.5  per  cent  solution  of  gelatin  chloride  or  gelatin 
sulphate  will  increase  the  less  at  20°  the  lower  the  pH  of  the  solu- 
tion. Figure  58  shows  that  this  is  the  case. 

In  Chap.  XIV  we  shall  see  that  the  rate  of  solution  of 
powdered  gelatin  in  water  is  influenced  in  a  different  way  by 
different  salts.  Na2SO4  diminishes  the  rate  of  solution  of 
powdered  gelatin  chloride  when  the  concentration  of  Na2SO4 
exceeds  M/64;  and  the  diminution  is  the  greater  the  higher  the 
concentration;  while  CaCl-2  accelerates  the  rate  of  solution  of 
powdered  gelatin  chloride  when  the  concentration  of  CaC^ 
exceeds  M/4. 

Gelatin  chloride  solutions  of  pH  3.4,  containing  1  gm.  of 
originally  isoelectric  gelatin  in  100  c.c.  solution,  were  made  up  in 
various  concentrations  of  Na2SO4  and  CaCl2.  The  solutions 
were  rapidly  heated  to  45°  and  rapidly  cooled  to  20°C.  and  kept 
at  this  temperature  for  1  hour.  The  time  of  outflow  of  the 
solution  through  a  viscometer  was  measured  immediately  and 
in  intervals  of  5  or  10  minutes.  The  time  of  outflow  of  water 
through  the  viscometer  at  20°  was  61  seconds. 

The  viscosity  of  a  gelatin  chloride  solution  of  pH  3.4  rises 
gradually  but  very  slowly  (uppermost  curve  in  Fig.  59)  and  the 
rate  of  increase  of  viscosity  on  standing  is  not  materially  altered 
in  M/512  Na2SO4  and  only  little  in  M/128  Na2SO4.  In  M/32 
Na2SO4  the  viscosity  increases  more  rapidly  on  standing,  in 
M/8  Na2SO4  still  more  rapidly,  and  in  M/2  Na2SO4  very  sharply. 
This  is  exactly  what  we  should  expect,  since  the  Na2SO4  causes  a 
diminution  of  the  rate  of  solution  of  gelatin  chloride  as  soon  as 
the  concentration  of  Na2SO4  is  above  M/64.  In  such  solutions 
the  rate  of  solution  of  micellae  will  be  less  and  less,  and  since 
new  micellae  are  constantly  formed  at  20°C.  the  viscosity  will 
rise  more  rapidly  on  standing  when  the  solution  contains  Na2SO4 
in  concentrations  above  M/64  than  when  the  solution  contains 
less  Na2SO4  or  none  at  all. 

Figure  60  shows  that  CaCl2  in  concentrations  up  to  M/8  does 
not  alter  the  increase  in  viscosity  of  gelatin  chloride  solution  on 
standing,  but  that  the  viscosity  of  gelatin  chloride  of  pH  3.4  no 


VISCOSITY 


219 


longer  increases  on  standing  when  the  concentration  of  CaCU  is 
M/2  or  1  M.  In  this  concentration  CaCl2  causes  a  slight  increase 
in  the  rate  of  solution  of  gelatin  chloride. 

NaCl  causes  no  change  in  the  rate  of  solution  of  gelatin  chloride 
as  long  as  the  concentration  of  NaCl  does  not  exceed  1  M. 
Above  this  concentration  it  causes  coagulation  and  the  viscosity 


Influence  of  CaCl2  on 
the  rise  in  viscosity  of 
1%  gelatin  chloride 
solution  of  pH  3.4  on 
standing   at  20 °C. 


2.7 

2.6 

2.5 

2.4 

2.3 

S  2.2 
^  2.1 
8  2.0 

.2  L9 

^  1.8 
1.7 
1.6 
1.5 

1.4 

5  10  15  20  25  30  35  40  45  50  55  60 

Time  in  minutes 

FIG.  60. — Showing  that  concentrations  of  CaCh  or  M/2  or  above  prevent 
the  increase  in  viscosity  of  gelatin  chloride  solution  of  pH  3.4  on  standing 
at  20°C. 

can  no  longer  be  measured.  Hence  NaCl  in  concentrations  up 
to  1  M  should  not  alter  the  rate  of  increase  of  viscosity  of  gelatin 
chloride  solutions  on  standing.  Figure  61  shows  that  this  is 
correct. 

The  simplest  method  of  melting  solid  particles  of  jelly  is  by 
heating  to  45°C.  If,  therefore,  the  striking  increase  in  viscosity 
which  occurs  when  a  0.5  per  cent  solution  of  isoelectric  gelatin  is 


220 


THEORY  OF  COLLOIDAL  BEHAVIOR 


kept  standing  for  a  day  at  a  temperature  of,  e.g.,  10°C.,  is  due  to 
the  formation  of  particles  of  solid  jelly,  then  if  this  solution  is 
heated  to  45°C.  and  cooled  rapidly  to  20°C.  the  majority  of  these 
solid  particles  should  have  melted  and  dissolved  into  isolated 


I 


2.7 
2.6 
2.5 
2.4 
2.3 

zz 


o    1>9 

>  I1? 

.1.6 

1.5 
1.4 
1.3 
1.2 
1.1 


i    i    r 


i    i    i 


Influence  of  NaCl  on 
the  rise  in  viscosity  of 
17o  gelatin  chloride 
solution  of  pH  3.4  on 
standing    at   20°  C 


0  5 


10  15  20  25  30  35  40  45  50  55  60 

Time  in  minutes 

FIG.  61. — Showing  that  NaCl  solutions  up  to  a  concentration  of  1M  have  no 
effect  on  the  increase  in  viscosity  of  gelatin  chloride  solution  of  pH  3.4  on  stand- 
ing at  20°C. 

ions  or  molecules.  Hence  such  a  solution  when  cooled  rapidly 
to  20°  should  show  at  this  temperature  a  considerably  lower 
viscosity  than  the  same  solution  shows  at  20°  when  it  is  brought 
to  this  temperature  directly  from  10°C.  without  previous  heating 
to  45°C.  The  experiment  represented  in  Fig.  62  shows  that  this  is 
the  case. 


VISCOSITY 


221 


These  experiments  then  support  the  conclusion  that  the  high 
viscosity  of  gelatin  solutions  and  the  influence  of  electrolytes  on 
this  viscosity  is  due  to  the  fact  that  these  solutions  contain  sub- 
microscopic  particles  of  solid  jelly  (micellae)  capable  of  occluding 
large  amounts  of  water  the  quantity  of  which  is  regulated  by  the 
Donnan  equilibrium. 

4.  The  pH  influences  the  viscosity  of  casein  chloride  solutions 
in  a  similar  way  to  that  in  which  it  influences  gelatin  chloride 


3.5 
o    3.0 

^  2'5 
8 
|    2'° 

1.5 
1.0 

. 

sCe' 

JKX 

l£h 

?r|/ 

r^^ 

^P 

^ 

^^^% 

Vx 

? 

/ 

/ 

^ 

^ 

Vi 

sec 

sit- 

/"    C 

f 

\ 

^ 

0* 

>7o^ 

HO' 

elal 
citic 

in  c 
>n  8 

hlo 

rid 

T, 

s 

\ 

i 

/ 

' 

\ 

«r 

\ 

-£ 

t?e\ 

iou 

?iy 

ke 

^>M 

f 

n1 

» 

i 

0^ 

<ru 

—  u~ 

u^t 

•o  — 

Lfl 

r  u 

0  

•   •• 

!__    -^ 

>-^*" 

pH  1.8  2.0  22   2.4  2.6   2.8  3.0  32  34  3.6   3.8  4.0  42  4.4  4.6 

FIG.  62. — Showing  that  previous  heating  diminishes  the  viscosity  of  0.5  per  cent 
solutions  of  gelatin  chloride. 


solutions;  and  the  depressing  effect  of  neutral  salts  on  the  vis- 
cosity of  casein  chloride  solutions  is  similar  to  that  of  the  addition 
of  salts  on  the  osmotic  pressure  of  gelatin  chloride.  Casein 
chloride  solutions  have  no  tendency  to  set  to  a  jelly,  but  they 
have  one  feature  in  common  with  gelatin  solutions,  namely,  the 
existence  of  particles  capable  of  occluding  water,  the  amount  of 
which  is  regulated  by  the  Donnan  equilibrium.  As  a  conse- 
quence, casein  chloride  solutions  have  a  comparatively  high 
viscosity  which  is  influenced  by  electrolytes  in  the  way  charac- 
teristic for  the  Donnan  equilibrium.  The  existence  of  such 


222 


THEORY  OF  COLLOIDAL  BEHAVIOR 


particles  in  the   casein   chloride   solution  is  indicated  by  the 
opacity  of  the  solution. 

The  material  used  in  our  experiments  was  a  fine  dry  powder  of 
nearly  isoelectric  casein  prepared  after  Van  Slyke  and  Baker. 
Particles  of  equal  size  of  grain  (between  mesh  100  and  120)  were 
sifted  out  and  1  gm.  of  such  powder  was  put  into  100  c.c.  each 
of  solutions  of  HC1  of  different  concentration  to  bring  the  casein 
to  varying  pH.  A  microscopic  examination  of  the  granules 


22 

8    E0 

S     18 

.»-> 

g     16 

.9     14 


1 

I 


10 
8 
6 
4 


Volune  ofscdimen 


incc. 


pH  1.4    1.6   1.6  20  2.2  2.4  2.6   28  3.0  32  3.4  3.6  3.8  4.0  4.2 

FIG.  63. — Swelling  and  solution  of  casein  chloride  in  1  and  22  hours  at  20°C. 

showed  that  they  underwent  a  swelling  which  was  a  minimum 
at  the  isoelectric  point,  which  increased  with  increasing  hydrogen 
ion  concentration  until  it  reached  a  maximum,  and  which  then 
diminished  again  with  a  further  increase  in  the  hydrogen  ion 
concentration  (see  Chap.  XV).  Hence,  the  volume  of  the 
casein  particles  suspended  in  the  HC1  varied  in  a  similar  way 
with  the  pH  as  the  volume  of  suspended  particles  of  gelatin. 

This  swelling  could  also  be  observed  when  the  suspension  was 
put  into  100  c.c.  graduates  and  the  suspended  particles  were 
allowed  to  settle. .  The  volume  of  the  sediment  was  a  minimum 
at  the  isoelectric  point  increasing  with  increasing  hydrogen  ion 


VISCOSITY 


223 


concentration  of  the  solution  and  finally  decreasing  again.  But 
the  curves  of  swelling  and  of  volume  of  sediment  were  only 
parallel  at  the  beginning  of  the  experiment,  since  the  swelling 
(which  occurred  at  once)  was  followed  by  some  of  the  casein 
going  into  solution  or  into  suspension.  The  longer  the  experi- 
ment lasted  the  smaller  the  volume  of  the  sediment  became  and 
the  larger  the  mass  which  went  into  the  supernatant  solution. 
This  is  expressed  in  Fig.  63.  The  upper  curve  represents  the 
volume  of  the  sediment  after  1  hour.  The  suspension  of  1  gm.  of 


Dry  weight  of  sediment  in  £m 

i>*  to  to  •£>  bt  b>  ^  b» 
ooooooooo 

& 

x^ 

k 

& 

f 

N> 

L 

$ 

7 

$1 

\ 

\ 

^ 

/ 

£ 

TT 

s^ 

s 

v^ 

X 

ty 

; 

\ 

<& 

vv 

/ 

Dr 

y  v 

/•eif 

htc 

)fsc 

5dir 

ien 

*\ 

J> 

7 

in  j 

|m. 

"O*-o 

pH  1.4  L6    16   2.0   22  2.4  2.6   2.8  3.0  3.2  3.4  3.6  "3.8  4.0  4.2 

FIG.  64. — Dry  weight  of  sediment  of  casein  chloride  solutions  after  1  and  22 

hours. 

casein  in  100  c.c.  of  HC1  of  different  concentration  had  been  kept 
for  1  hour  at  20°,  had  been  shaken  repeatedly  but  not  frequently, 
and  the  suspension  was  then  passed  into  100  c.c.  graduates  and 
allowed  to  settle  at  20°C.  After  2  hours  the  volume  of  the  sedi- 
ment was  measured  and  the  volumes  are  the  ordinates  of  the 
curve  marked  " after  1  hour"  in  Fig.  63.  A  similar  experiment 
was  made  in  which  the  suspension  of  casein  was  kept  for  22 
hours  at  20°C.  and  was  allowed  to  settle  during  6  hours  also  at 
20°C.  The  volumes  are  the  ordinates  of  the  second  curve  in 
Fig.  63,  marked  "  after  22  hours."  The  abscissae  are  the  pH 
of  the  total  solution  and  suspension. 

The  curve  " after  1  hour"  is  clear,  since  it  is  chiefly  the  expres- 


224  THEORY  OF  COLLOIDAL  BEHAVIOR 

sion  of  the  variation  of  the  degree  of  swelling  of  the  casein 
particles,  not  as  much  having  gone  into  solution  as  after  22 
hours.  We  notice  that  the  volume  occupied  by  the  solid  particles 
in  the  1-hour  curve  is  a  minimum  at  the  isoelectric  point,  that  it 
rises  steeply  after  pH  3.1,  that  it  drops  at  2.2,  and  that  a  second 
drop  commences  at  pH  1.8.  The  two  drops  have  a  different 
cause.  The  drop  at  pH  1.8  is  due  to  a  diminution  of  the  degree 
of  swelling  of  the  sediment,  while  the  drop  at  2.2  in  the  1-hour 
curve  is  due  to  the  fact  that  at  pH  2.2,  where  the  solubility  of 
casein  chloride  is  a  maximum,  some  of  the  casein  chloride  has  gone 
into  solution.  This  conclusion  is  supported  by  the  fact  that  the 
drop  at  2.2  increases  in  time  and  is  very  considerable  after  22 
hours  (see  Fig.  63),  while  otherwise  the  1-hour  and  the  22-hour 
curves  show  only  minor  differences. 

The  proof  that  this  interpretation  in  the  volume  curves  of  Fig. 
63  is  correct  is  furnished  by  Fig.  64,  where  the  ordinates  are  the 
dry  weights  of  the  sediments,  the  volumes  of  which  are  given  in 
Fig.  63.  One  gram  of  powdered  casein  had  when  dried  for  24 
hours  at  between  90  and  100°C.  a  dry  weight  of  0.87  gm. 

That  part  of  the  casein  chloride  which  goes  into  the  supernatant 
liquid  (i.e.,  which  is  not  contained  in  the  sediment)  consists  of 
two  constituents,  namely,  first,  solid  submicroscopic  particles  in 
suspension  which  in  due  time  would  have  settled,  and  second, 
isolated  casein  ions  and  molecules.  The  solid  particles  in  the 
supernatant  liquid  (unless  they  are  below  the  limit  required  to 
occlude  water)  undergo  the  same  swelling  under  the  influence  of 
the  Donnan  equilibrium  as  the  particles  of  the  sediment.  In 
addition,  however,  we  have  individual  casein  ions  in  solution  (the 
molecules  being  probably  insoluble  since  isoelectric  casein  is 
practically  insoluble)  but  these  ions  cannot  undergo  any  swelling 
and  hence  do  not  add  materially  to  the  volume  and  the  viscosity. 
As  a  consequence,  the  more  solid  particles  of  casein  chloride  are 
dissolved  into  isolated  casein  ions  or  particles  too  small  to  occlude 
water,  the  more  the  relative  volume  occupied  by  the  casein  in 
the  solution  should  be  diminished,  and  this  should  be  accompanied 
by  a  diminution  in  viscosity.  If  our  theory  of  the  origin  of  the 
viscosity  of  the  gelatin  solutions  is  correct,  it  should  be  possible 
to  prove  that  where  the  solubility  of  the  casein  chloride  solution 
is  a  maximum  the  viscosity  curve  shows  a  drop. 


VISCOSITY 


225 


The  correctness  of  this  inference  is  supported  by  the  viscosity 
curves  in  Fig.  65,  which  represent  the  viscosity  after  1  hour  and 
after  22  hours.  The  experiments  are  the  same  as  those  referred 
to  in  Figs.  63  and  64.  The  viscosity  of  the  total  suspension  and 
solution  was  measured  in  a  straight  viscosimeter  with  a  time  of 
outflow  for  water  of  48.4  seconds  at  20°C.  The  curve  for  the 
viscosities  after  1  hour  is  the  expression  chiefly  of  the  swelling, 
since  casein  chloride  goes  only  slowly  into  solution  at  20°C. 
The  curve  is  almost  continuous  and  has  its  maximum  in  the 
region  between  pH  2.1  and  2.4,  where  also  the  swelling  is  a 


1.7 

.2    L6 
b 

W     1-3 

1     12 
?     1.1 

1.0 
pHl 

FIG.  65.— 

/ 

*  * 

r~^» 
# 

s* 

^v? 

\ 

Vi 

sec 

sit^ 

rof 

1% 

&- 

-cr-c 

x^, 

^\ 

S 

ca 

sei: 

A 

1  C 

(•  p/ 

hloi 

?id€ 

*y 

V* 

K 

s 

t 

\ 

jr 

3 

4  1.6    1.8   2.0   22  2.4  2.6   2.8   3.0   3.2  3.4  3.6  3.8  40  4.2 

Viscosity  of  1  per  cent  casein  chloride  solutions  after  1  and  22  hour 
at  20°C. 

maximum.     There  is,  however,  a  slight  depression  at  pH  2.2, 
where  the  solubility  of  the  casein  is  a  maximum. 

The  curve  for  the  viscosities,  Fig.  65,  after  22  hours  shows,  how- 
ever, a  distinct  saddle  at  pH  2.2  where  the  solubility  of  casein 
chloride  is  a  maximum.  This  agrees  with  the  assumption  that 
the  high  viscosity  is  due  to  swollen  particles  of  casein,  a  certain 
quantity  of  which  had  been  dissolved  at  or  near  pH  2.2.  This 
solution  of  the  particles  capable  of  swelling  beneath  that  size 
where  they  no  longer  can  occlude  water  must  diminish  the  rela- 
tive volume  of  the  casein  and  cause  a  diminution  of  the  viscosity. 
Below  a  pH  of  1.8,  where  the  solubility  of  the  casein  is  consider- 
ably diminished,  the  1-hour  and  the  22-hours  viscosity  curves 
(Fig.  65)  no  longer  differ  materially.  As  a  consequence  of  the 

15 


226 


THEORY  OF  COLLOIDAL  BEHAVIOR 


saddle  the  maximum  of  the  viscosity  curve  after  22  hours  now 
lies  at  pH  2.6. 

Since  the  point  at  issue,  namely,  the  diminution  of  the  viscosity 
when  solid  submicroscopic  particles,  capable  of  swelling,  are 
dissolved  into  particles  so  small  that  they  no  longer  can  occlude 
water,  is  so  fundamental  for  the  theories  of  viscosity  and  of 
colloidal  behavior  in  general,  it  seemed  necessary  to  look  for  a 
more  striking  proof  than  that  given  in  the  experiment  quoted. 
For  this  purpose  measurements  were  made  on  1  per  cent  casein 
chloride  solutions  prepared  from  very  finely  powdered  casein 
particles  sifted  through  a  200-mesh  sieve.  In  order  to  get  a 


1.0 


pHl4    1.6    1.8  2.0   2.2    2.4  2.6    2.8  3.0   3.2   3.4    3.6  3.8  4.0  4.2 


FIG. 


66. — Diminution  of  viscosity  through  solution  of  solid  particles  of  casein 

chloride. 


more  rapid  solution  of  the  particles  the  experiment  was  carried 
out  at  40°C.  The  time  of  outflow  of  water  through  the  visco- 
meter  at  40°  was  35.5  seconds.  Figure  66  gives  the  results. 
The  viscosity  measurements  were  made  at  four  different  times, 
namely:  first,  immediately  after  the  powdered  casein  was  put 
into  the  HC1;  then  after  1J^,  3,  and  6  hours.  During  this  time 
the  casein  chloride  solutions  were  kept  at  40°C.  The  viscosity 
curve  taken  immediately  after  the  suspensions  were  prepared  is 
continuous  and  is  the  expression  of  the  swelling  which  occurred 
in  the  few  minutes  which  elapsed  in  the  preparation  of  the  suspen- 
sions and  during  which  the  casein  was  at  40°C.  The  maximum 
swelling  occurred  at  about  pH  2.3.  At  this  time  the  amount  of 


VISCOSITY 


227 


casein  dissolved  into  separate  casein  ions,  was  negligible.  The 
curve  resembles  the  1-hour  curve  in  Fig.  65.  After  1^  hours  the 
second  measurements  of  viscosity  were  taken,  and  the  reader  will 
notice  from  Fig.  66  that  the  viscosity  had  dropped  considerably 
in  the  neighborhood  of  pH  2.2  where  the  solubility  of  casein  chlo- 
ride is  the  greatest,  and  the  maximum  depression  is  at  pH  2.1 
where  also  the  solubility  is  a  maximum.  With  a  further  lower- 
ing of  the  pH  the  viscosity  rises  again.  The  maximal  viscosity 
in  the  IJ^-hours  series  is  now  at  pH  of  about  2.7  or  2.8  where  it 


«QJD 


20 
18 
16 

14 

5 

10 

8 

e^— 

4 

50 
40 
30 
20 
10 
0 

/ 

7  * 

N 

V 

• 

J/ 

d 

\ 

\ 

J 

^S 

s\ 

{ 

5 

\ 

X 

f 

\\ 

? 

V 

6 
4 

2 

0 
pHi 

^ 

l\0 

§ 

y 

oCt 

sei 

n  c 

ilor 

ide 

U 

^ 

kp 

* 

4    1.6    1.8    2/3    22    24    2.6  26   3.0    3.2  3.4 

FIG.  67. — Similarity  of  curves  for  log  —  and  for  relative  volume  of  casein  chloride 

770 
in  solutions. 

was  also  in  the  22-hours  series  in  Fig.  65.  The  later  viscosity 
measurements,  after  3  and  6  hours  (Fig.  66)  confirm  these  conclu- 
sions. 

5.  It  is  of  interest  to  see  whether  or  not  Arrhenius's  formula 
can  account  for  the  influence  of  electrolytes  on  the  viscosity  of 
casein  suspensions.     If  this  were  the  case,  the  curves  represent- 
ing log  -  should  run  parallel  to  curves  representing  the  relative 
770 

volume  occupied  by  the  casein  in  the  solution.  We  get  the 
values  of  log  —  from  our  observations  of  the  relative  viscosity 


228  THEORY  OF  COLLOIDAL  BEHAVIOR 

which  give  us  — ,  aird  we  can  calculate  the  volume  from  the 

'no 

measured  volume  of  the  sediment  plus  the  calculated  volume  of 
the  casein  in  the  supernatant  liquid.  The  latter  value  is  obtained 
by  deducting  the  dry  weight  of  the  sediment  from  the  (known) 
dry  weight  of  the  whole  mass  of  casein  put  into  the  water  (1  gm. 
powdered  casein,  dry  weight  =  0.87  gm.);  assuming  that  the 
casein  in  the  supernatant  liquid  consists  exclusively  of  suspended 
particles.  This  is  partly  correct  for  a  1-hour  experiment  at  20°. 
The  ordinates  in  Fig.  67  represent  the  values  for  volume  thus 

corrected  and  the  values  for  log  —  while  the  abscissae  are  the  pH 

"no 

of  the  suspensions.     The  two  curves  are  almost  parallel. 

It  should  be  stated  that  these  corrected  volumes  of  casein 
include  a  certain  amount  of  water  between  the  granules.  We 
are,  however,  in  this  case  not  concerned  with  the  absolute  but 
only  the  relative  volume  occupied  by  the  casein. 

When  NaCl  is  added  in  different  concentrations  to  a  casein 
chloride  solution  it  is  noticed  that  the  viscosity  is  diminished 
as  it  is  in  the  case  of  solutions  of  gelatin  chloride.  We  shall  see 
in  Chap.  XV  that  this  diminution  of  viscosity  is  accompanied  by 
a  diminution  in  the  degree  of  swelling  of  the  individual  particles 
of  casein  which  is  parallel  to  the  depression  of  the  viscosity. 

One  gram  of  powdered  casein  was  put  into  100  c.c.  of  H2O 
containing  12.5  c.c.  of  0.1  N  HC1,  and  NaCl  in  concentrations 
varying  from  0  to  M/4.  The  mixture  was  shaken  occasionally 
and  kept  for  16  hours  at  20°.  Then  the  viscosity,  volume  of 
sediment  (after  settling  for  24  hours),  dry  weight  of  sediment 
(after  deduction  of  the  free  NaCl  contained  in  the  sediment) 
were  determined.  When  the  volume  and  the  values  for  log 

—  are  plotted  as  ordinates  over  the  concentrations  as  abscissae, 

7° 

it  is  found  that  the  two  curves  agree  fairly  well  (Fig.  68)  except 

where  no  or  little  salt  was  added  and  where  therefore  some  casein 
particles  had  been  completely  dissolved.  In  this  solution  the 
calculated  volume  was  too  high  and  our  curves  express  the  fact. 
From  these  experiments  we  may  conclude  that  the  influence  of 
electrolytes  on  the  viscosity  of  casein  solutions  or  suspensions  is 
due  to  the  swelling  of  particles  of  casein  suspended  in  the  solu- 


VISCOSITY 


229 


tion  of  casein  and  that  the  volume  of  these  particles  is  regulated 
by  the  Donnan  equilibrium. 

6.  These  experiments  leave  little  doubt  that  the  high  viscosity 
of  certain  protein  solutions,  such  as  gelatin  or  casein,  is  due  to  the 
existence  of  solid  particles  occluding  large  quantities  of  water, 
the  amount  of  which  is  regulated  by  the  Donnan  equilibrium, 
while  the  isolated  ions  of  proteins  in  solution  or  the  particles  too 
small  to  occlude  water  have  no  share  in  the  causation  of  high 
viscosities. 


22 
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Concentration  of  NaCl 

in  solutions. 

The  quantities  of  water  which  can  be  occluded  in  a  solid  jelly 
of  gelatin  are  enormous.  If  we  assume  the  molecular  weight 
of  gelatin  to  be  of  the  order  of  magnitude  of  about  12,000,  a 
solid  gel  of  1  per  cent  originally  isoelectric  gelatin  contains  over 
60,000  molecules  of  water  to  1  molecule  of  gelatin.  It  is  out  of 
the  question  that  such  masses  of  water  could  be  held  by  the 
secondary  valency  forces  of  the  gelatin  and  water  molecules. 
Casein  particles  occlude  much  less  water  and  for  this  reason  the 


230  THEORY  OF  COLLOIDAL  BEHAVIOR 

viscosity  of  casein  chloride  solutions  never  becomes  as  high  as 
that  of  gelatin  solutions  containing  equal  masses  of  protein  per 
100  c.c.  of  solution. 

All  the  experiments  described  agree  with  the  occlusion  theory 
but  not  with  the  hydration  theory.  Thus  the  fact  that  the 
viscosity  of  a  0.5  per  cent  solution  of  isoelectric  gelatin  increases 
rapidly  at  a  temperature  of  20°C.  or  below  cannot  possibly  be 
explained  on  the  basis  of  the  hydration  theory  since  isoelectric 
gelatin  is  not  ionized.  It  might  be  explained  on  the  basis  of 
another  suggestion  which  attributes  to  the  gelatin  solution  a 
similar  structure  to  that  possessed  by  the  solid  jelly  of  gelatin. 
This  idea  would  lead  us  to  the  assumption  that  in  addition  to  the 
source  of  viscosity  due  to  the  relative  volume  of  the  protein 
solution  there  exists  a  second  type  peculiar  to  protein  solutions 
which  has  no  connection  with  the  volume. 

"Bearing  in  mind  the  possibility  that  protein  solutions  may  contain  a 
preformed  molecular  structure  analogous  to  that  of  the  jellies  or  coagula 
which  they  can  form,  we  are  strongly  impelled  towards  the  belief  that  the 
type  of  viscosity  which  solutions  of  proteins  exhibit  may  in  some  manner 
owe  its  existence  to  this  structure,  and  not  to  the  type  of  internal  friction 
which  hinders  molecular  and  ionic  motion.  Thus  a  netlike  structure, 
such  as  a  tennis  net,  will  offer  no  hindrance  to  the  passage  through  it  of  a 
quickly  moving  body  which  is  smaller  than  its  meshes,  other  than  that 
which  is  due  to  the  fact  that  the  material  which  composes  the  net  occu- 
pies a  small  fraction  of  the  area  which  the  body  must  traverse,  but  to 
any  force  which  involves  deformation  of  the  structure,  for  instance,  a 
force  which  seeks  to  drag  it  through  a  small  tube,  it  will  offer  a  very 
considerable  resistance."1 

This  theory  becomes  untenable  in  the  case  of  suspensions  of 
powdered  gelatin  and  of  casein  chloride  which  have  no  tendency 
to  set  to  a  jelly.  It  fails,  moreover,  to  account  for  the  fact  that 
the  influence  of  pH  on  the  viscosity  resembles  that  on  the  osmotic 
pressure  of  gelatin  solutions.  The  assumption  of  a  second 
type  of  viscosity  independent  of  the  relative  volume  occupied 
by  the  solute  becomes  unnecessary,  since  the  theories  of  Einstein 
and  of  Arrhenius  respectively,  which  derive  the  viscosity  from  the 
relative  volume,  suffice  to  account  for  all  the  phenomena  observed. 

1  ROBERTSON,  T.  B.,  "The  Physical  Chemistry  of  Proteins,"  pp.  324-25, 
New  York,  London,  Bombay,  Calcutta,  and  Madras,  1918. 


VISCOSITY  231 

We  therefore  arrive  at  the  conclusion  that  where  the  hydrogen 
ion  concentration,  the  valency  of  ions,  and  the  concentration  of 
salts  influence  the  viscosity  of  protein  solutions  in  a  similar  way 
to  that  in  which  they  influence  the  osmotic  pressure,  this  influence 
on  viscosity  is  in  reality  an  influence  of  electrolytes  on  the  swelling 
of  solid  submicroscopic  protein  particles  contained  in  the  solution. 


CHAPTER  XIII 

A   RECIPROCAL   RELATION   BETWEEN   THE    OSMOTIC 

PRESSURE  AND  THE  VISCOSITY  OF  GELATIN 

SOLUTIONS1 

1.  The  experiments  in  the  preceding  chapter  have  led  to  the 
conclusion  that  proteins  form  true  solutions  consisting  of  isolated 
protein  ions  and  molecules  which  may  or  may  not  contain  in 
addition  to  the  isolated  ions  and  molecules  submicroscopic 
particles  capable  of  occluding  water  and  giving  rise  to  a  Donnan 
equilibrium.  Only  when  a  protein  solution  contains  particles  of 
this  latter  type  do  we  notice  a  comparatively  high  viscosity  and  a 
similar  influence  of  electrolytes  on  viscosity  as  on  osmotic  pres- 
sure. Solutions  of  crystalline  egg  albumin  of  not  too  high  a  con- 
centration have  a  comparatively  low  viscosity  which  is  not 
affected  in  the  typical  way  by  electrolytes  and  this  leads  to  the 
conclusion  that  these  solutions  consist  chiefly  of  isolated  ions  and 
molecules  or  of  particles  too  small  to  occlude  water.  If  this  con- 
clusion is  justified,  we  are  forced  to  the  further  conclusion  that  the 
influence  of  electrolytes  on  the  osmotic  pressure  of  protein  solu- 
tions is  determined  by  the  isolated  ions  of  a  protein  solution  and 
not  by  the  submicroscopic  particles  capable  of  occluding  water, 
i.e.,  the  micellae,  since  solutions  of  crystalline  egg  albumin  show 
the  influence  of  electrolytes  on  their  osmotic  pressure  in  a  striking 
way.  It  would  further  follow  that  in  case  of  a  gelatin  solution 
where  both  isolated  ions  and  submicroscopic  micellae  are  sup- 
posed to  exist  the  isolated  ions  are  responsible  for  the  influence  of 
electrolytes  on  the  osmotic  pressure  of  the  solution  while  the  sub- 
microscopic  particles  of  solid  jelly  capable  of  occluding  water  are 
responsible  for  the  influence  of  electrolytes  on  the  viscosity  of 
gelatin  solutions.  In  other  words,  wherever  there  exists  a  rever- 
sible aggregate  formation  from  isolated  protein  ions  in  solution 

1  LOEB,  J.,  J.  Gen.  Physiol,  vol.  4,  p.  97,  1921-22, 

232 


OSMOTIC  PRESSURE  AND  VISCOSITY  233 

there  should  exist  a  reciprocal  relation  between  the  viscosity  and 
the  osmotic  pressure  of  the  solution  since,  the  transformation  of 
the  submicroscopic  particles  of  solid  jelly  should  lower  the  vis- 
cosity and  raise  the  osmotic  pressure  of  a  gelatin  solution  and 
vice  versa.  It  can  be  shown  that  this  conclusion  is  supported  by 
observations  on  gelatin  solutions. 

It  was  noticed  in  the  preceding  chapter  that  the  viscosity  of 
solutions  of  gelatin  chloride  does  not  always  increase  on  standing 
but  that  it  diminishes  when  the  temperature  exceeds  a  certain 
limit.  This  was  shown  for  a  2  per  cent  solution  of  gelatin  chloride 
of  pH  2.7  in  Fig.  57.  The  viscosity  of  such  a  solution  increases 
very  rapidly  on  standing  at  15°C.,  much  less  rapidly  at  25°C., 
but  diminishes  when  kept  at  a  temperature  above  35°C.,  and  the 
more  rapidly  the  higher  the  temperature.  This  we  assume  tobe 
due  to  the  fact  that  at  a  temperature  above  35°C.  the  rate  of 
melting  of  submicroscopic  particles  of  solid  jelly  exceeds  the  rate 
of  their  formation  from  isolated  ions  or  molecules. 

Several  liters  of  a  0.55  per  cent  solution  of  isoelectric  gelatin 
were  kept  at  about  10°C.  for  48  hours  and  at  20°C.  for  the  next 
24  hours.  Then  the  stock  solution  was  divided  into  two  parts. 
The  one  part  was  subdivided  into  doses  of  90  c.c.  each,  and  each 
was  brought  to  a  different  pH  by  adding  10  c.c.  containing 
different  quantities  of  HC1.  In  this  way  the  concentration  of 
originally  isoelectric  gelatin  was,  therefore,  in  every  case  0.5 
per  cent.  The  second  portion  was  treated  in  the  same  way 
except  that  before  adding  the  acid  the  gelatin  was  kept  for  1 
hour  at  45°C.  This  was  done  to  melt  part  of  the  submicroscopic 
pieces  of  jelly  assumed  to  exist  in  the  solution,  and  thus  to 
increase  the  concentration  of  the  isolated  ions  and  molecules  and 
to  diminish  the  relative  quantity  of  solid  submicroscopic  particles 
responsible  for  the  high  viscosity  characteristic  of  gelatin  solu- 
tions. After  this  second  portion  of  the  stock  solution  of  iso- 
electric gelatin  had  been  kept  for  1  hour  at  45°C.  it  was  rapidly 
cooled  to  20°C.,  the  HC1  was  added  in  the  way  described  for  the 
first  portion  and  the  solutions  were  put  into  collodion  bags  to 
measure  the  osmotic  pressure.  Each  collodion  bag  contained 
about  50  c.c.  of  gelatin  solution.  The  temperature  now  remained 
constant  at  20°C.  for  both  sets  of  experiments.  It  was  noticeable 
from  the  first  that  the  osmotic  pressure  of  the  gelatin  solution 


234 


THEORY  OF  COLLOIDAL  BEHAVIOR 


which  had  been  kept  for  1  hour  at  45°  and  which  was  therefore 
supposed  to  have  melted  into  smaller  particles  was  higher  than 
that  of  the  gelatin  solution  not  previously  heated.  Figure  69 
shows  the  result  after  22  hours.  The  maximum  osmotic  pressure 
was  for  the  gelatin  solution  that  had  been  previously  heated  200 
mm.  H2O,  while  it  was  only  170  mm.  for  the  other  gelatin  solution 
not  previously  heated  to  45°C. 


220 


1.8  2.0  2.2  2.4  2.6  2.8  3.0  3.2  3.4  Z.Q  3.6  4.0  4.2  4.4  4.6 

FIG.  69. — Showing  that  the  osmotic  pressure  of  a  solution  of  gelatin  chloride 
which  has  been  previously  heated  to  45°C.  for  1  hour  and  then  rapidly  cooled 
to  20°C.  is  higher  than  the  osmotic  pressure  of  the  same  solution  of  gelatin 
chloride  not  previously  heated. 

Then  the  viscosities  were  determined  at  20°  and  they  gave  the 
opposite  result  (Fig.  62  of  the  preceding  chapter),  the  viscosities 
being  considerably  higher  in  the  solutions  not  previously  heated 
to  45°  than  in  the  solutions  previously  heated.  This  experiment 
then  confirms  our  expectation  that  there  exists  a  reciprocal 
relation  between  the  viscosity  of  protein  solutions  and  their 
osmotic  pressure,  inasmuch  as  a  transformation  of  solid  sub- 
microscopic  particles  of  jelly  into  isolated  protein  ions  and  mole- 
cules diminishes  the  viscosity  but  increases  the  osmotic  pressure. 

As  far  as  the  quantitative  relations  are  concerned,  the  differ- 


OSMOTIC  PRESSURE  AND  VISCOSITY  235 

ence  in  viscosity  (Fig.  62)  is  more  striking  than  the  difference  in 
osmotic  pressure  (Fig.  69).  This  is  possibly  connected  with  the 
fact  that  the  lowering  in  viscosity  due  to  heating  to  45°C.  was 
measured  immediately  after  the  temperature  had  reached  20°C. 
again,  while  the  osmotic  pressure  of  the  same  solutions  was 
measured  after  the  solutions  had  been  standing  for  22  hours  at 
20°C.  During  this  time  a  considerable  formation  of  sub- 
microscopic  particles  of  solid  jelly  had  probably  occurred  in  the 
solutions  previously  heated  to  45°C. 

It  was  expected  that  when  we  put  a  collodion  bag  filled  with  a 
1  per  cent  solution  of  gelatin  of  e.g.,  pH  3.5,  which  had  been  kept 
for  1  hour  at  45°  and  cooled  to  20°  into  a  beaker  containing  a  1 
per  cent  solution  of  the  identical  gelatin  chloride  solution  of  pH 
3.5,  but  which  had  not  been  heated  to  45°C.  before  being  brought 
to  20°C.,  water  would  diffuse  from  the  latter  into  the  former 
solution.  This  experiment  was  carried  out  with  a  positive  result. 

These  experiments  support  the  idea  expressed  in  the  preceding 
chapter  that  protein  solutions  are  true  solutions  which  may  or 
may  not  contain  solid  particles  of  protein  capable  of  swelling. 
In  the  case  of  gelatin  solutions  the  formation  of  submicroscopic 
particles  of  solid  jelly  from  isolated  molecules  or  ions  is  a  reversi- 
ble process,  and  this  leads  in  this  case  to  a  reciprocal  variation  of 
osmotic  pressure  and  viscosity  of  such  solutions. 

This  probably  explains  a  phenomenon  which  has  puzzled  the 
writer  for  a  long  time,  namely  that  the  osmotic  pressures  of 
gelatin  solutions  of  the  same  pH  and  concentration  of  originally 
isoelectric  gelatin  showed  occasionally  variations  for  which  he 
could  not  account.  It  now  becomes  probable  that  this  was  due 
to  a  factor  which  was  not  taken  into  consideration,  namely, 
that  on  standing  at  room  temperature  a  gradual  transformation 
of  isolated  molecules  or  ions  into  larger  aggregates  takes  place, 
which  must  diminish  the  osmotic  pressure  but  increase  the 
viscosity.  This  source  of  variation  was  eliminated  in  the  viscos- 
ity experiments  in  which  the  gelatin  solution  was  always  heated 
first  to  45°C.  and  then  as  soon  as  this  temperature  was  reached 
the  solution  was  cooled  to  the  temperature  desired  for  the  viscos- 
ity measurements.  It  is  probable  that  the  same  uniformity  of 
treatment  is  also  required  for  the  osmotic  pressure  experiments. 

This  reciprocal  relation  between  osmotic  pressure  and  viscosity 


236  THEORY  OF  COLLOIDAL  BEHAVIOR 

exists  probably  also  in  the  case  of  solutions  of  casein  salts. 
Solutions  of  Na  caseinate  are  less  opaque  than  those  of  casein 
chloride  (of  the  same  concentration  of  originally  isoelectric 
casein)  which  indicates  that  the  Na  caseinate  solution  contains 
more  isolated  casein  ions  and  fewer  submicroscopic  solid  particles 
than  the  solution  of  casein  chloride. 

The  writer  had  already  shown  in  a  preceding  chapter  that  the 
maximal  viscosity  of  a  1  per  cent  solution  of  casein  chloride  is 
higher  than  the  viscosity  of  solutions  of  Na  caseinate  of  equal 
concentration  of  originally  isoelectric  casein,  while  the  osmotic 
pressures  of  solutions  of  the  two  salts  show  exactly  the  reverse 
relation,  the  maximal  osmotic  pressure  of  a  1  per  cent  solution 
of  Na  caseinate  being  almost  700  mm.  H^O  while  the  maximal 
osmotic  pressure  of  a  1  per  cent  solution  of  casein  chloride  is 
only  about  200  mm. 

The  solutions  of  crystalline  egg  albumin  seem  to  consist  (at 
ordinary  temperature  and  at  not  too  high  a  concentration  of 
albumin  and  of  the  hydrogen  ions)  exclusively  or  almost  exclu- 
sively of  isolated  molecules  or  ions.  Since  the  latter  cannot 
diffuse  through  a  collodion  membrane  they  give  rise  to  a  Donnan 
equilibrium  across  the  membrane  and  hence  only  the  osmotic 
pressure  of  solutions  of  salts  of  crystalline  egg  albumin  is  influ- 
enced by  electrolytes  in  the  way  demanded,  while  the  viscosity 
shows  such  an  influence  only  to  a  negligible  degree. 

2.  It  should  be  possible  to  give  a  more  striking  confirmation 
of  the  reciprocal  relation  between  the  viscosity  and  the  osmotic 
pressure  if  we  replace  in  a  gelatin  solution  part  of  the  dissolved 
gelatin  by  equal  weight  of  powdered  gelatin.  Such  a  substitu- 
tion should  increase  the  viscosity  and  diminish  the  osmotic 
pressure  of  the  solution. 

Figure  70  shows  that  the  osmotic  pressure  of  a  1  per  cent  solu- 
tion of  originally  isoelectric  gelatin  diminishes  the  more  the  more 
we  replace  the  dissolved  gelatin  by  small  granules  of  powdered 
gelatin.  The  ordinates  of  the  upper  curve  represent  the  values 
of  the  osmotic  pressure  of  a  1  per  cent  solution  of  originally 
isoelectric  gelatin  at  different  pH,  the  pH  serving  as  abscissae  of 
the  curves.  The  acid  used  was  HC1,  and  the  curve  is  the  usual 
one.  At  the  beginning  of  the  experiment  the  gelatin  solution  was 
rapidly  heated  to  a  temperature  of  45°C.  and  rapidly  cooled  to 


OSMOTIC  PRESSURE  AND  VISCOSITY 


237 


20°C.  and  then  kept  at  that  temperature  throughout  the  entire 
experiment.  The  pH  is  that  of  the  gelatin  solution  at  the  end  of 
the  experiment. 

The  middle  curve  represents  an  experiment  in  which  0.5  gm. 
of  the  isoelectric  gelatin  in  solution  was  replaced  by  0.5  gm.  of 


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pH  1.6    16  2.0  2.2  24  26  25  3.0  3.2  3.4  3.6  3.8  40  42  4.4  4.6 

FIG.  70. — A  suspension  of  1  gm.  of  a  fine  powder  of  gelatin  in  100  c.c.  of 
water  has  practically  no  osmotic  pressure  (lowest  curve),  while  a  solution  of 
1  gm.  of  the  same  gelatin  has  a  maximal  osmotic  pressure  of  over  500  mm. 
(uppermost  curve).  A  mixture  of  0.5  gm.  of  powdered  and  0.5  gm.  of  liquid 
gelatin  in  100  c.c.  water  has  practically  the  osmotic  pressure  of  the  0.5  per  cent 
liquid  gelatin  in  100  c.c.  of  water  (middle  curve). 


isoelectric  powdered  gelatin.  The  latter  did  not  contribute  to 
the  osmotic  pressure,  the  observed  osmotic  pressure  being  due  to 
the  isolated  ions  of  the  0.5  per  cent  gelatin  in  solution  which 
determined  the  Donnan  effect,  and  in  addition  to  the  gas  pres- 


238  THEORY  OF  COLLOIDAL  BEHAVIOR 

sure  of  the  isolated  gelatin  ions  and  the  isolated  gelatin  molecules. 
Theoretically,  of  course,  the  coarse  particles  of  gelatin  also 
participate  in  the  osmotic  pressure  but  this  effect  is  negligible  on 
account  of  the  small  number  of  such  particles.  (The  gelatin 
particles  used  were  of  grain  size  slightly  above  %o  of  an  inch 
diameter.)  At  the  beginning  of  the  experiment  the  0.5  per 
cent  solution  of  gelatin  was  rapidly  heated  to  45°C.  and  rapidly 
cooled  to  20°C.,  and  then  the  powdered  gelatin  was  added.  The 
pH  is  that  of  the  0.5  per  cent  gelatin  solution  at  the  end  of  the 
experiment. 

The  lowest  curve  represents  the  osmotic  pressure  of  1  gm.  of 
powdered  isoelectric  particles  in  100  c.c.  of  HC1  of  different  pH. 
The  slight  osmotic  pressure  observed  is  probably  due  to  the  fact 
that  a  little  of  the  gelatin  went  gradually  into  solution.  This 
apparently  happened  to  a  less  extent  in  a  repetition  of  this  experi- 
ment and  the  osmotic  pressures  observed  were  still  lower  than  in 
the  lowest  curve  in  Fig.  70.  All  these  osmotic  pressure  experi- 
ments were  made  in  a  thermostat  at  20°C. 

The  viscosity  is  affected  in  exactly  the  opposite  sense  from  the 
osmotic  pressure  if  part  of  the  dissolved  gelatin  is  replaced  by 
solid  particles  of  gelatin.  The  more  dissolved  gelatin  is  replaced 
by  solid  particles  of  gelatin  the  higher  the  viscosity,  a  result 
to  be  expected  from  the  experiments  and  conclusions  already 
stated. 

Solutions  of  0.5,  0.625,  0.750,  0.875,  and  1.0  gm.  of  isoelectric 
gelatin  were  heated  quickly  to  45°C.  and  cooled  quickly  to  20°C., 
and  so  much  powdered  gelatin  of  pH  7.0  was  added  as  to  bring 
the  total  gelatin  in  100  c.c.  to  1  gm.;z.e.,  to  a  0.5  per  cent  solution 
of  gelatin  was  added  0.5  gm.  of  powdered  gelatin  (between  mesh 
sizes  100  and  120),  and  to  a  0.875  per  cent  solution  of  liquid 
gelatin  was  added  0.125  gm.  of  powdered  gelatin,  while  no 
powdered  gelatin  was  added  to  the  1  per  cent  solution  of  liquid 
gelatin.  The  different  mixtures  were  brought  to  different  pH 
through  the  addition  of  different  quantities  of  HC1  and  the  solu- 
tions were  allowed  to  stand  for  1  hour  before  the  viscosities  were 
measured  in  order  to  give  the  powdered  gelatin  a  chance  to  swell. 
The  results  of  the  measurements  are  represented  in  Fig.  71. 
The  reader  will  see  that  within  the  range  of  the  pH  between  3.6 
and  1.4  the  viscosity  is  the  greater,  the  more  liquid  gelatin  is 


OSMOTIC  PRESSURE  AND  VISCOSITY 


239 


replaced  by  powdered  gelatin.  This  supports  the  idea  that 
the  influence  of  electrolytes  on  the  viscosity  of  gelatin  solutions 
is  due  to  the  influence  of  the  electrolytes  on  the  swelling  of  solid 
submicroscopic  particles  of  gel  in  the  solution. 

The  nature  of  the  curves  in  Fig.  71  between  pH  4.6  and  3.8 
requires  an  explanation.     The  curves  are  here  the   lower  the 


pH  1.4  1.6  1.8  ED  2.2   E4   £6  2.6  3.0   3.2  3.4  3.6  3.8  4.0  42  4.4  4.6 


FIG.  71.  —  The  influence  of  replacing  liquid  by  powdered  gelatin  on  viscosity 
is  exactly  the  reverse  as  on  osmotic  pressure.  The  more  the  powdered  particles 
replace  the  liquid  gelatin  the  higher  the  viscosity. 

more  liquid  gelatin  is  replaced  by  solid  gelatin.  This  is  due  to 
the  fact  that  it  was  necessary  to  let  the  suspensions  stand  for  at 
least  1  hour  to  allow  the  particles  of  powdered  gelatin  to  swell 
before  the  viscosity  measurements  were  made.  During  this 
time  the  liquid  gelatin  at  or  near  the  isoelectric  point  increases 


240 


THEORY  OF  COLLOIDAL  BEHAVIOR 


rapidly  in  viscosity  while  this  increase  in  viscosity  is  suppressed 
where  the  hydrogen  ion  concentration  is  higher.  This  is  proved 
by  Fig.  72  which  gives  the  viscosity  of  the  supernatant  solutions 
of  gelatin  (without  the  suspended  particles)  which  had  been  stand- 
ing for  1  hour.  Inside  the  range  of  pH  4.4  and  4.6  the  viscosity 
had  risen  more  rapidly  on  standing  than  at  the  lower  pH ;  which 
means  that  at  or  near  the  isoelectric  point  new  submicroscopic 
particles  of  solid  jelly  are  constantly  formed  from  the  molecules 
while  this  process  is  the  slower  the  higher  the  hydrogen  ion 
concentration.  While  thus  the  addition  of  acid  to  a  solution  of 
isoelectric  gelatin  retards  the  rate  of  formation  of  new  submicro- 


0.8' 


5% 


0.62  5  2 


V1£CO£ 


pH  1.4  16  Ifl  20  2.2  2.4  2.6  26  3.0  32  3.4  3.6  38  40  42  4.4  4.6 

FIG.  72. — Viscosity  of  gelatin  solutions  after  standing  for  1  hour  at  20°C. 
Notice  minimum  at  pH  4.4,  indicating  that  the  viscosity  has  risen  more  near  the 
isoelectric  point  on  account  of  the  formation  of  submicroscopic  particles  of  gel. 

scopic  particles  of  jelly,  it  increases  the  swelling  of  those  already 
present  when  the  acid  is  added.  On  the  other  hand,  powdered 
particles  of  isoelectric  gelatin  in  water  of  pH  4.7  do  not  increase 
their  volume  on  standing. 

The  fact  that  the  addition  of  acid  to  a  solution  of  isoelectric 
gelatin  inhibits  or  retards  the  formation  of  new  solid  particles 
on  standing  was  discussed  in  the  preceding  chapter. 

If  we  now  return  to  .the  discussion  of  the  curves  in  Fig.  71  we 
may  say  that  the  results  in  that  part  of  the  curves  which  belongs 
to  the  abscissae  of  pH  above  3.8  is  the  expression  of  the  fact  that 
that  part  of  the  viscosity  which  is  due  to  the  gelatin  in  solution 


OSMOTIC  PRESSURE  AND  VISCOSITY 


241 


had  undergone  an  increase  during  the  hour  the  solution  had  been 
standing  at  20°C.  after  having  been  heated  to  45°C.;  and  that  the 
increase  caused  in  the  viscosity  of  the  liquid  gelatin  was  a  maxi- 
mum at  the  isoelectric  point,  being  almost  zero  at  a  pH  below  3.4; 
while  the  addition  of  acid  had  the  opposite  effect  on  the  solid 
granules  of  gelatin,  since  their  volume  was  increased  according 
to  the  rules  of  the  Donnan  equilibrium. 

It  is  necessary  that  we  convince  ourselves  that  a  Donnan  equi- 
librium exists  when  particles  of  solid  gelatin  are  suspended  in  a 
solution  of  gelatin.  That  this  is  actually  true  was  shown  in  the 
following  way:  0.5-gm.  doses  of  powdered  gelatin  were  added  to 
100  c.c.  of  0.5  per  cent  gelatin  chloride  solutions  of  different  pH. 
The  different  beakers  containing  these  mixtures  were  kept  for  3^ 
hours  at  20°C.  The  mass  was  then  filtered  through  cotton  wool 
and  the  pH  of  the  filtrate  (0.5  per  cent  gelatin  solution)  and  of  the 
solid  gelatin  granules  were  determined,  that  of  the  latter  after 
they  had  been  melted.  It  was  found  that  the  pH  of  the  gelatin 
granules  was  higher  than  that  of  the  solution  and  that  the  differ- 
ence followed  the  Donnan  equilibrium  equation  (Table  XLIV), 
though  the  result  was  slightly  irregular  owing  to  the  fact  that  it 
is  impossible  to  free  the  suspended  particles  of  gelatin  completely 
from  the  supernatant  liquid.  When  we  separate  a  gelatin  solu- 
tion from  water  by  a  collodion  membrane  we  have  two  equilib- 
ria, one  across  the  membrane  caused  by  the  protein  ions  on  one 
side  of  the  membrane;  and  a  second  one  inside  the  protein  solu- 
tion caused  by  the  solid  particles  of  jelly. 

TABLE  XLIV 


pH  of  gelatin  in 

suspension  

5.12 

4.60 

4.49 

4.18 

4.07 

3.73 

3.45 

3.93 

2.68 

2.34 

2.09 

1.86 

1.77 

1.53 

pH  of  gelatin  in 

solution  

4.98 

4.35 

4.12 

3.91 

3.69 

3.50 

3.14 

2.78 

2.50 

2.28 

1.97 

1.86 

1.72 

1.57 

The  reciprocal  relation  between  viscosity  and  osmotic  pressure 
of  protein  solutions  disposes  of  the  attempt  to  explain  the  influ- 
ence of  electrolytes  on  the  physical  properties  of  protein  solu- 
tions on  the  basis  of  the  micella  or  aggregate  theory.  We  have 
seen  that  both  the  osmotic  pressure  of  a  gelatin  chloride  solution 
as  well  as  its  viscosity  are  depressed  when  a  neutral  salt  is  added 


16 


242  THEORY  OF  COLLOIDAL  BEHAVIOR 

to  the  solution.  The  micella  theory  would  explain  this  by  assum- 
ing that  the  addition  of  a  salt  increases  the  degree  of  aggregation 
in  the  solution  and  hence  diminishes  the  number  of  isolated  par- 
ticles and  therefore  the  osmotic  pressure  of  the  solution.  This 
assumption  cannot  be  put  to  a  quantitative  test  since  we  have  no 
direct  method  of  determining  the  number  of  aggregates  in  solu- 
tion. We  have  shown,  however,  in  this  chapter  that  if  we  in- 
crease the  number  of  aggregates  at  the  expense  of  isolated  protein 
ions  or  molecules,  the  viscosity  rises.  Hence,  if  we  assume  that 
the  number  of  aggregates  in  the  gelatin  chloride  solution  is 
increased  through  the  addition  of  salt,  the  viscosity  of  such  a 
solution  should  increase  for  the  same  reason;  whereas  in  reality 
we  have  seen  that  the  addition  of  salt  depresses  both  the  osmotic 
pressure  and  the  viscosity  of  the  gelatin  solution.  This  fact 
eliminates  the  aggregation  or  micella  theory  as  a  possible  source 
of  explanation  of  the  colloidal  behavior.  We  need  not  deplore  the 
loss,  since  the  application  of  the  aggregate  theory  to  the  explana- 
tion of  colloidal  phenomena  has  never  risen  beyond  the  stage  of 
vague  speculations. 


CHAPTER  XIV 
THE  STABILITY  OF  PROTEIN  SOLUTIONS1 

A.  THE   STABILITY  OF   WATERY   AND  AQUEOUS  SOLUTIONS  OF 

GELATIN 

1.  It  is  difficult  to  discuss  the  problem  of  the  stability  of 
colloidal  solutions  satisfactorily  as  long  as  we  do  not  possess  a 
complete  theory  of  the  solution  of  crystalloids.  In  a  general  way 
we  can  say  that  there  seem  to  exist  two  different  kinds  of  forces 
by  which  substances  can  be  kept  in  solution,  first,  the  general 
forces  active  in  all  solutions  and  which  are  supposed  to  be  the 
forces  of  attraction  between  solvent  and  solute;  and  second,  the 
special  forces  such  as  the  mutual  repulsion  of  the  particles  due  to 
electrical  charges.  These  latter  special  forces  are  supposed  to 
become  of  significance  only  when  the  general  forces  of  attraction 
between  solute  and  solvent  are  comparatively  feeble. 

It  was  noticed  long  ago  that  colloids  in  general  and  proteins  in 
particular  behave  very  differently  in  regard  to  the  concentration 
of  salt  required  for  precipitation,  some  requiring  very  high  con- 
centrations of  salt  for  this  purpose  and  others  comparatively  low 
concentrations.2  There  is  apparently  no  transition  between  the 
two  extremes.  It  was  formerly  believed  that  these  differences 
in  the  concentration  of  salts  required  could  be  used  for  the  classi- 
fication of  colloids,  and  some  authors  divide  the  proteins  or 
colloids  in  general  into  two  groups,  those  which  exist  in  the  form 
of  suspensions  ("suspensoids,"  "lyophobic"  or  "  hydrophobic " 
colloids),  and  those  which  exist  in  the  form  of  solutions  ("emul- 
soids,"  "lyophilic"  or  " hydrophilic "  colloids).  The  former  are 
precipitated  by  low  concentrations,  the  latter  only  by  high  con- 
centrations of  salt.  It  is  of  more  interest  to  know  the  reason 
why  the  precipitation  of  one  type  requires  high  and  of  the  other 

1LoEB,  J.,  and  LOEB,  R.  F.,  J.  Gen.  PhysioL,  vol.  4,  p.  187,  1921-22. 
2  HARDY,  W.  B.,  J.  PhysioL,  vol.  33,  p.  251,  1905-06. 

243 


244  THEORY  OF  COLLOIDAL  BEHAVIOR 

low  concentrations  of  salts  than  to  invent  names  for  the  two 
cases. 

We  intend  to  show  that  where  low  concentrations  of  electro- 
lytes are  required  for  precipitation,  the  precipitating  influence 
of  the  salt  has  the  earmarks  of  the  Donnan  effect,  inasmuch  as 
the  effective  ion  of  the  salt  has  the  opposite  sign  of  charge  to  that 
of  the  protein  particles,  while  where  high  concentrations  of  salts 
are  required  no  such  relation  exists;  and  we  conclude  from  this 
that  where  low  concentrations  of  salts  suffice  for  precipitation, 
the  precipitation  is  due  to  the  diminution  of  the  value  (pH  inside 
the  colloidal  particles  minus  pH  of  the  outside  solution),  as  shown 
in  the  chapter  on  the  charge  of  colloidal  particles,  while  where  high 
concentrations  of  salts  are  required  the  precipitating  influence  is 
due  to  some  other  cause,  possibly  the  weakening  of  the  forces  of 
attraction  between  protein  molecules  and  the  molecules  of  the 
solvent,  e.g.,  water,  through  the  presence  of  the  salt.  This  latter 
conclusion,  of  course,  would  imply  that  the  proteins  can  exist  in 
true  crystalloidal  solution,  the  ultimate  units  being  protein 
molecules  or  ions.  There  is  no  proof  against  the  permissibility 
of  such  an  assumption  in  the  case  of  aqueous  solutions  of  crystal- 
line egg  albumin  (at  the  proper  temperature,  pH,  and  concentra- 
tion) or  of  gelatin.  This  opinion  is  shared  by  S0rensen,  who  has 
not  hesitated  to  determine  the  molecular  weight  of  crystalline 
egg  albumin  from  the  osmotic  pressure  of  its  solution.1 

2.  Solutions  of  gelatin  in  water  require  enormous  concentra- 
tions of  salts  for  precipitation,  and  this  process  of  salting  out  has 
no  connection  with  the  Donnan  equilibrium,  since  solutions  of 
gelatin  are  more  readily  salted  out  by  sulphates  than  by  chlorides 
regardless  of  the  pH  of  the  protein  solution.  The  same  is  true 
for  solutions  of  crystalline  egg  albumin  of  pH  4.7  or  above;  when, 
however,  the  pH  of  the  crystalline  egg  albumin  becomes  too  low 
(e.g.,  2.0  or  less),  lower  concentrations  of  salts  will  cause  precipita- 
tion. The  reason  for  this  influence  of  the  pH  is  mentioned  at 
the  end  of  this  chapter. 

Eight-tenths  per  cent  solutions  of  gelatin  were  prepared  at 
three  different  pH,  namely  4.7  (isoelectric  gelatin),  3.8  (gelatin 
chloride),  and  6.4  to  7.0  (Na  gelatinate).  The  purpose  was  to 

1  S0RENSEN,  S.  P.  L.,  Studies  on  proteins;  Compt.  rend.  trav.  Lab.  Carlsberg, 
vol.  12,  Copenhagen,  1915-17. 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


245 


find  the  molecular  concentration  of  different  salts — namely, 
(NH4)2SO4,  Na2SO4,  MgSO4,  KC1,  and  MgCl2— required  for  pre- 
cipitation. Table  XLV  shows  that  regardless  of  the  pH  the 
sulphates  are  better  precipitants  than  the  chlorides.  Wherever 
we  are  dealing  with  colloidal  phenomena,  i.e.,  phenomena  regu- 
lated by  the  Donnan  equilibrium,  we  must  expect  that  sulphates 
will  have  a  more  depressing  effect  than  chlorides  when  the  protein 
is  on  the  acid  side  of  the  isoelectric  point  but  no  when  it  is  on  the 
alkaline  side  or  at  the  isoelectric  point.  But  this  is  not  true  for 
the  influence  of  ions  on  the  salting  out  of  gelatin  in  aqueous 
solution. 

TABLE    XLV. — MINIMAL    MOLAR   CONCENTRATIONS    REQUIRED    TO    PRE- 
CIPITATE 0.8  PER  CENT  SOLUTIONS  OF  GELATIN 


pH  of  gelatin  solution 

Approximate  molecular  concentration  of  salt 
required  for  precipitation 

(NH4hSO4 

Na2SO4 

MgS04 

KC1 

MgCh 

4  7 

>Kf»M 

XK6    M 
^6    M 

%  M 

K  M 
H  M 

*%  M 

H  M 
H  M 

>3  M 
3  M 
>3  M 

>3  M 
>3  M 

>3  M 

3  8  (gelatin  chloride) 

6  4  to  7  0  (Na  gelatinate) 

The  question  arises,  How  does  it  happen  that  sulphates  are 
better  precipitants  than  chlorides?  Some  light  is  thrown  on 
this  fact  by  experiments  on  the  rate  of  solution. 

Powdered  gelatin  of  not  too  small  a  size  of  grain  (going  through 
sieve  30  but  not  through  sieve  60)  was  rendered  isoelectric  in  the 
way  described  in  Chap.  II  and  about  0.8  gm.  was  put  into  100 
c.c.  of  each  of  a  series  of  solutions  of  NaCl,  CaCl2,  or  Na2SO4, 
varying  in  concentration  from  M/4,096  to  2  M.  The  suspensions 
of  the  powdered  gelatin  were  frequently  stirred  and  the  time 
required  to  practically  completely  dissolve  all  the  grains  of 
powdered  gelatin  in  suspension  at  35°C.  was  measured.  The 
ordinates  in  Fig.  73  are  the  solution  times  of  isoelectric  gelatin, 
and  the  abscissae  are  the  molecular  concentrations  of  the  salt 
used.  It  is  obvious  that  NaCl  and  still  more  CaCl2  increase  the 
rate  of  solution  of  isoelectric  gelatin  in  water,  and  the  more  the 
higher  the  concentration  of  the  salts  added.  There  exists, 
however,  a  striking  discontinuity  in  the  Na2SO<  curve.  As  long 


246 


THEORY  OF  COLLOIDAL  BEHAVIOR 


as  the  concentration  of  Na2SO4  is  below  M/32  it  increases  the 
solubility  of  gelatin,  and  the  more  so  the  higher  the  concentration. 
When,  however,  the  concentration  of  Na2SO4  is  above  M/32,  a 
further  increase  in  the  concentration  of  Na2SO4  diminishes  the 
solubility  of  gelatin  and  the  more  so  the  higher  the  concentration 
of  Na2S04.  (NH4)2SO4  acts  like  Na2SO4.  We  now  understand 


I 


130 
120 

no 

100 
90 
80 
70 
60 
50 
40 
30 
20 
10 


( 

Influence  of  salts  on 
solution  time  of  0.87o 
isoelectric  gelatin 
at  35  °C. 

Eg 

\1 

5? 

V 

\ 

\ 

v 

r 

^ 

S. 

\ 

1 

#< 

N 

\s 

\ 

4 

V 

1 

"S 

(^ 

V 

^ 

N*. 

LK 

^f 

ls>z 

r* 

t 

^ 

Nr 

x 

\< 

\ 

N 

N 

\, 

i 

^ 
1 

H 

y 

< 

^, 

K*««( 

\ 

*  f  «  f 

Concentration  of  salts 

FIG.  73. — Influence  of  salts  on  the  time  required  for  the  solution  of  0.8  gm. 
of  powdered  isoelectric  gelatin  in  100  c.c.  salt  solution  at  35°C.  and  pH  4.7. 
Notice  difference  of  curve  for  Na2$O4  and  for  CaCh  and  Nad. 

why  we  cannot  precipitate  solutions  of  isoelectric  gelatin  with 
KC1  or  MgCl2  in  concentrations  up  to  3  M  (see  Table  XLV)  while 
we  can  precipitate  such  solutions  with  sulphates  but  only  at 
concentrations  above  M/2. 

It  may  be  of  interest  to  supplement  these  observations  by  the 
results  given  in  Table  XLVa,  on  the  influence  of  salt  solutions 
of  three  different  molar  concentrations,  namely,  M/1,024,  M/512, 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


247 


and  M/256,  on  the  time  required  to  dissolve  0.8  gm.  of  powdered 
isoelectric  gelatin  at  35°C.  The  salt  solutions  had  a  pH  of  4.7. 
It  is  obvious  from  the  table  that  the  dissolving  power  of  the 
chlorides  increases  with  the  valency  of  the  cation  while  the  dissolv- 
ing power  of  the  Na  salts  increases  with  the  valency  of  the  anion. 

TABLE  XLVo. — TIME   IN   MINUTES   REQUIRED  TO  DISSOLVE  0.8  GM.  OF 
POWDERED  ISOELECTRIC  GELATIN  AT  35°C. 


M/256 

M/512 

M/1,024 

LiCl  

57 

70 

76 

NaCl                   

49 

66 

75 

KC1 

56 

70 

80 

MgCl2       

32 

40 

61 

CaCl2                                 

32 

40 

62 

BaCl2 

31 

46 

66 

CeCl2                        

26 

35 

44 

LaCl3 

23 

Na2SO4             

34 

46 

60 

Na4Fe  (CN)6 

24 

32 

41 

While  isoelectric  gelatin  is  only  sparingly  soluble,  gelatin 
salts  are  highly  soluble.  Doses  of  0.8  gm.  of  powdered  gelatin 
of  pH  of  about  3.3  dissolve  very  rapidly  in  100  c.c.  HC1  of  the 
same  pH  at  35°C.  The  addition  of  NaCl  or  CaCl2  no  longer 
increases  the  solubility,  except  for  CaCU  in  concentrations  above 
M/16.  Na2SC>4  or  (NH^SC^  abruptly  diminishes  the  solubility 
at  a  concentration  above  M/4;  and  NaCl  does  so  above  a  con- 
centration of  1  M  (Fig.  74). 

Figure  75  shows  the  influence  of  the  three  salts  on  the  solution 
time  of  Na  gelatinate  of  pH  10.5.  Na2SO4  diminishes  the  solu- 
bility abruptly  at  a  concentration  above  M/8  while  both  NaCl 
and  CaCU  increase  the  solubility  of  Na  gelatinate,  NaCl  in 
concentrations  above  M/2,  and  CaCl2  in  concentrations  above 

M/16. 

In  all  three  cases,  therefore,  is  the  solubility  of  gelatin  dim- 
inished by  sulphates,  but  only  exceptionally  by  chlorides.  This 
explains  the  results  contained  in  Table  XLV.  The  solubility 
of  gelatin  in  water  does  not  depend  on  the  Donnan  equilibrium. 


248 


THEORY  OF  COLLOIDAL  BEHAVIOR 


This  conclusion  is  supported  by  an  investigation  of  the  influence 
of  the  pH  on  the  solubility  of  gelatin. 

We  have  seen  that  addition  of  little  acid  to  isoelectric  gelatin 
increases  the  osmotic  pressure,  viscosity,  P.D.,  and  swelling, 
while  beyond  a  certain  pH  the  addition  of  more  acid  has  a  depress- 


gelatin chloride  pH  3.3 
at  35°  C. 


Concentration  of  salts 

FIG.  74. — Influence  of  salt  on  solution  time  of  0.8  gm.  of  powdered  gelatin 
chloride  of  pH  3.3  in  100  c.c.  salt  solution  at  pH  3.3.  The  gelatin  is  no  longer 
soluble  beyond  1M  NaCl. 

ing  effect.  It  was  of  interest  to  find  out  whether  such  a  maximum 
followed  by  a  drop  existed  in  the  influence  of  acid  on  the  solu- 
bility of  gelatin.  This  is  not  the  case  at  least  between  pH  4.7 
and  1.0,  since  the  solubility  increases  steadily  with  increasing 
hydrogen  ion  concentration,  as  was  proven  by  measurements  of 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


249 


the  dry  weight  of  gelatin  dissolved  in  a  certain  time  at  different 
pH.  This  corroborates  the  conclusion  that  the  solution  (and 
precipitation)  of  gelatin  in  water  is  not  influenced  by  forces 
governed  by  the  Donnan  equilibrium  and  does  therefore  not 
show  the  characteristics  of  colloidal  behavior.  We  are  probably 
dealing  in  this  case  with  forces  of  residual  valency  between  water 


Influence  of  salts  on 

solution  time  of  0.6  % 

Na  gelatinate  pH  10.5 

at  35°  C. 


Concentration  of  salts 

Fio.  75. — Influence  of  salts  on  solution  time  of  0.8  gm.  of  powdered  Na  gelatinate 
in  100  c.c.  salt  solution  at  pH  10.5. 

and  gelatin  molecules,  these  forces  being  increased,  as  a  rule,  by 
the  addition  of  salt  to  water,  with  the  exception  of  the  sulphates, 
which  diminish  the  forces  when  added  beyond  a  certain  concen- 
tration at  which  the  chlorides  do  not  cause  a  diminution  in 
solubility.  This  explains  why  it  is  easier  to  salt  out  gelatin 
from  its  aqueous  solutions  by  sulphates  than  by  chlorides. 


250  THEORY  OF  COLLOIDAL  BEHAVIOR 

These  experiments  also  show  that  the  solution  of  solid  gelatin 
does  not  depend  upon  swelling  (while  the  solution  of  casein 
chloride  is,  as  we  shall  see,  determined  by  swelling).  The  swelling 
of  gelatin  in  acid  reaches  a  maximum  at  pH  of  about  2.8  and  then 
diminishes  upon  further  increase  in  hydrogen  ion  concentration, 
while  the  rate  of  solution  of  solid  gelatin  granules  continues  to 
increase  steadily  when  the  hydrogen  ion  concentration  increases 
beyond  pH  of  2.8  down  to  pH  1.0  (and  possibly  less).  The 
mechanism  of  swelling  and  the  mechanism  of  solution  of  solid 
gelatin  in  solutions  of  acid  or  alkali  are  determined  by  forces  of 
an  entirely  different  character;  the  swelling  by  osmotic  pressure, 
and  the  solution  in  all  probability  by  those  forces  which  are 
responsible  for  the  solution  of  crystalloids.  The  role  of  secondary 
valency  forces  in  the  process  of  solution  is  suggested  by  the  follow- 
ing quotation  from  Langmuir. 

"Acetic  acid  is  readily  soluble  in  water  because  the  COOH  group 
has  a  strong  secondary  valency  by  which  it  combines  with  water. 
Oleic  acid  is  not  soluble  because  the  affinity  of  the  hydrocarbon  chains 
for  water  is  less  than  their  affinity  for  each  other.  When  oleic  acid 
is  placed  on  water  the  acid  spreads  upon  the  water  because  by  so  doing 
the  COOH  can  dissolve  in  the  water  without  separating  the  hydrocarbon 
chains  from  each  other. 

"When  the  surface  on  which  the  acid  spreads  is  sufficiently  large  the 
double  bond  in  the  hydrocarbon  chain  is  also  drawn  onto  the  water 
surface,  so  that  the  area  occupied  is  much  greater  than  in  the  case  of 
the  saturated  fatty  acids. 

"Oils  which  do  not  contain  active  groups,  as  for  example  pure  paraffin 
oil,  do  not  spread  upon  the  surface  of  water."1 

It  should  be  added  that  if  we  replace  the  H  in  the  carboxyl 
group  of  oleic  acid  by  K  the  very  soluble  potassium  oleate  is 
formed,  so  that  the  whole  molecule  is  now  dragged  into  the  water. 
The  Na  oleate  is  less  soluble  than  K  oleate.  Ca  oleate  is  again 
sparingly  soluble. 

In  the  case  of  proteins  we  have  to  deal  with  hydrocarbon 
groups  possessing  more  affinity  for  each  other  than  for  water, 
and  with  COOH  and  NH2  groups  (or  COO  and  NH3+  groups)  with 
a  strong  affinity  for  water.  It  is  probable  that  the  NH2  or 

1  LANGMUIR,  I.,  J.  Am.  Chem.  Soc.,  vol.  39,  p.  1850,  1917. 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  251 

NHj  groups  of  the  protein  molecule  are  more  active  on  the  acid 
side  of  the  isoelectric  point  and  the  COOH  or  COO  groups  on  the 
alkaline  side  of  the  isoelectric  point.  The  analogy  with  the  soaps 
would  also  suggest  that  the  nature  of  the  non-protein  ion  is  of 
importance  for  the  solubility  of  a  protein  salt.  This  is  found  to 
be  true  especially  in  the  case  of  casein-acid  salts,  casein  chloride 
being  more  soluble  than  casein  nitrate,  and  the  latter  more 
soluble  than  casein  trichloracetate. 

Until  evidence  to  the  contrary  is  furnished,  we  must  consider 
the  possibility  that  the  forces  keeping  proteins,  such  as  gelatin 
or  crystalline  egg  albumin,  in  aqueous  solutions  are  the  same  forces 
which  keep  crystalloids  in  solution.  The  fact  that  gelatin 
solutions  set  to  a  gel  does  not  necessarily  contradict  this  con- 
clusion. When  gelatin  solutions  approach  the  gel  state,  (i.e., 
when  they  reach  a  high  viscosity),  the  relative  distance  of  the 
protein  molecules  or  ions  from  each  other  remains  the  same  and 
the  affinity  of  the  active  groups  of  the  protein  ions  or  molecules 
for  water  is  not  changed.  The  concentration  of  salt  required 
for  precipitation  remains  also  practically  the  same. 

3.  At  the  isoelectric  point  the  affinity  of  certain  groups  of  the 
gelatin  molecule  for  water  is  a  relative  minimum,  as  is  shown  by 
the  fact  that  on  standing  at  not  too  high  a  temperature,  a  1  per 
cent  solution  of  isoelectric  gelatin  will  become  cloudy  and  the  sus- 
pended matter  will  settle;  while  this  will  not  happen  when  the 
pH  is  either  above  4.8  or  below  4.6.  When  a  little  alcohol  is 
added  to  such  a  solution  near  the  isoelectric  point,  a  rapid  pre- 
cipitation of  the  gelatin  occurs.  As  soon  as,  however,  the  pH 
is  4.4  or  below,  or  5.0  or  above,  the  gelatin  in  solution  remains 
soluble  even  with  an  excess  of  alcohol,  provided  the  anion  of  the 
acid  or  the  cation  of  the  alkali  added  to  the  isoelectric  gelatin  is 
monovalent  (in  the  range  of  pH  concerned),  e.g.,  Cl,  CH2COO, 
H2PO4,  HC204,  etc.,  or  Li,  Na,  K,  NH4.  When,  however,  these 
ions  are  bivalent,  e.g.,  SO4,  Ca,  Ba,  the  solubility  of  the  gelatin 
in  alcohol  is  much  less  and  the  addition  of  a  relatively  small 
amount  of  alcohol  will  cause  precipitation  of  the  gelatin.1  The 
addition  of  alcohol  diminished  the  attraction  between  the  watery 
groups  of  the  gelatin  molecule  or  ion  and  the  solvent,  and  where 
these  forces  are  small,  as  e.g.  at  the  isoelectric  point,  or  when  the 

1  LOEB,  J.,  J.  Gen.  PhysioL,  vol.  3,  p.  257,  1920-21. 


252  THEORY  OF  COLLOIDAL  BEHAVIOR 

ion  in  combination  with  the  gelatin  is  bivalent,  comparatively 
little  alcohol  suffices  for  precipitation  regardless  of  the  pH. 

On  the  other  hand,  the  addition  of  acid  with  monovalent  anion 
or  alkali  with  monovalent  cation  to  isoelectric  gelatin,  so  that  the 
pH  is  either  4.4  or  below  or  5.0  or  above  increases  the  power  of 
attraction  between  gelatin  and  water  to  such  an  extent  that  now 
the  1  per  cent  solution  of  originally  isoelectric  gelatin  becomes 
soluble  even  when  comparatively  much  alcohol  is  added. 

Isoelectric  crystalline  egg  albumin  remains  clear  in  solutions 
at  low  temperature,  e.g.,  2°C.,  for  many  months  even  in  a  con- 
centration of  8  per  cent.  When  the  temperature  is  raised,  a 
change  occurs  in  the  molecule  whereby  its  attraction  for  mole- 
cules of  water  is  diminished  and  a  1  per  cent  solution  precipitates 
at  pH  4.8  at  a  temperature  not  far  from  60°C.  (the  exact  tempera- 
ture was  not  ascertained).  This  precipitation  is  spoken  of  as  the 
heat  coagulation  of  egg  albumin.  If  we  add  slight  quantities  of 
HC1  the  temperature  at  which  the  coagulation  occurs  is  raised. 
At  pH  4.39  the  coagulation  occurs  on  rapid  heating  at  about  80°; 
at  pH  4.25  or  below  the  forces  of  attraction  between  the  molecules 
of  albumin  and  water  become  so  great  that  heat  coagulation  no 
longer  occurs  even  at  95°C. ;  the  solution  only  becomes  opalescent. 
It  was  found  that  the  pH  at  which  heat  coagulation  of  a  1  per  cent 
solution  of  crystalline  egg  albumin  no  longer  occurs  at  95°C.  is 
approximately  the  same  for  HC1,  HBr,  HNO3,  CH3COOH,  H3PO4, 
and  succinic  acid.  For  oxalic  and  tartaric  acids  it  is  only  slightly 
lower,  probably  because  at  this  pH  some  of  the  acid  anions  are 
bivalent.  The  main  fact  is,  that  for  H2SO4,  whose  anions  are  all 
bivalent,  the  pH  at  which  coagulation  becomes  impossible  is 
markedly  lower;  namely,  3.42.  All  this  is  in  harmony  with  the 
writer's  observations  on  the  effect  of  different  acids  on  the  solu- 
bility of  gelatin  in  alcohol-water  mixtures. 

On  the  alkaline  side  from  the  isoelectric  point  the  critical  pH 
at  which  heat  coagulation  disappears  is  practically  identical  for 
KOH  and  NaOH  while  the  pH  is  considerably  higher  for 
Ba(OH)2.1 

The  explanation  of  these  phenomena  is  a  part  of  the  general 
problem  of  solubility;  they  have  no  direct  connection  with  the 
theory  of  colloidal  behavior. 

1  Unpublished  results. 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  253 

4.  When  some  of  the  water  of  a  gelatin  chloride  or  Na  gelatin- 
ate  solution  is  replaced  by  ethyl  alcohol,  the  mechanism  which 
keeps  the  gelatin  in  solution  is  not  changed,  but  when  we  continue 
increasing  the  relative  amount  of  alcohol  in  the  solution  a  critical 
point  is  reached  where  the  amount  of  salt  required  for  the 
precipitation  changes  abruptly.1  We  must  conclude  that  the 
mechanism  by  which  the  gelatin  is  held  in  solution  changes  at  or 
near  this  critical  alcohol  concentration.  It  is  possible  to  show 
that  when  the  amount  of  alcohol  exceeds  the  critical  limit  the 
forces  guaranteeing  the  stability  of  the  solution  of  gelatin  in  the 
alcohol-water  mixture  are  the  forces  resulting  from  a  Donnan 
equilibrium. 

We  will  first  show  that  such  a  critical  point  exists  for  the  ratio 
water:  alcohol.  Ten  per  cent  solutions  of  gelatin  chloride  of 
pH  3.0  or  of  Na  gelatinate  of  pH  10.0  were  prepared.  Five 
cubic  centimeters  of  such  a  solution  were  first  warmed  to  liquefy 
the  gelatin  and  then  while  still  warm  they  were  diluted  with  45  c.c. 
of  a  mixture  of  alcohol  and  water;  the  relative  quantity  of  alcohol 
and  water  in  the  45  c.c.  varying.  Ten  cubic  centimeters  of  these 
1  per  cent  solutions  of  gelatin  chloride  or  Na  gelatinate  in  water- 
alcohol  were  titrated  with  a  solution  of  a  neutral  salt,  (NH4)2SO4, 
NaCl,  and  CaCl2,  at  20°C.  until  precipitation  occurred.  It  was 
noticeable  that  while  it  was  not  possible  to  precipitate  the  gelatin 
at  all  with  2%  M  CaCl2  or  5  M  NaCl  and  only  with  compara- 
tively high  concentrations  of  (NH4)2SO4  as  long  as  the  concentra- 
tion of  alcohol  did  not  exceed  a  certain  critical  value,  when  this 
critical  limit  was  exceeded  traces  of  these  salts  sufficed  for  pre- 
cipitation. This  is  illustrated  in  Tables  XLVI  and  XLVII. 
When  the  solution  contained  no  alcohol,  i.e.,  when  45  c.c.  of  H2O 
were  added  to  5  c.c.  of  the  10  per  cent  solution  of  gelatin  chloride 
of  pH  3.0,  7.1  c.c.  of  2  M  (NH4)2SO4  were  required  to  cause  pre- 
cipitation (Table  XLVI)  in  10  c.c.  of  the  1  per  cent  gelatin  chloride 
solution,  and  the  quantity  of  (NH4)2SO4  required  increased  at 
first  the  more  H2O  was  replaced  by  alcohol.  When  the  45  c.c.  of 
liquid  added  to  the  5  c.c.  of  10  per  cent  gelatin  solution  consisted 
of  18.75  c.c.  of  water  and  26.25  c.c.  of  ethyl  alcohol,  17.8  c.c.  of  2  M 
(NH4)2SO4  were  required  to  cause  precipitation  in  10  c.c.  of  the 
gelatin-alcohol-water  mixture,  but  if  now  the  proportion  of 

1  The  rest  of  this  chapter  is  based  on  experiments  not  yet  published. 


254 


THEORY  OF  COLLOIDAL  BEHAVIOR 


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THE  STABILITY  OF  PROTEIN  SOLUTIONS  255 

alcohol  to  water  was  shifted  only  slightly  in  favor  of  alcohol, 
namely  17.5  c.c.  of  water  and  27.5  c.c.  of  alcohol,  0.04  c.c.  instead  of 
17.8  c.c.  of  2  M  (NH4)2SO4  sufficed  for  precipitation  (Table  XL VI). 

In  the  case  of  NaCl  the  drop  was  still  more  striking.  When 
the  45  c.c.  added  to  the  5  c.c.  of  10  per  cent  gelatin  solution  con- 
sisted of  8.75  c.c.  of  water  and  36.25  c.c.  of  alcohol,  it  was 
impossible  to  cause  precipitation  in  10  c.c.  of  the  gelatin  chloride- 
alcohol-water  mixture  with  any  amount  of  5  M  NaCl.  When, 
however,  the  proportion  of  alcohol  was  only  slightly  increased, 
namely  7.5  c.c.  of  water  and  37.5  c.c.  of  alcohol,  0.2  c.c.  of  NaCl 
sufficed  for  precipitation.  In  the  case  of  CaCl2  the  critical  point 
was  reached  when  the  ratio  was  5  c.c.  of  water  and  40  c.c.  of 
alcohol. 

The  existence  of  the  critical  point  can  equally  well  be  demon- 
strated in  the  case  of  Na  gelatinate  as  is  shown  in  Table  XL VII. 

What  interests  us  is  the  following  fact.  The  mechanism  by 
which  gelatin  chloride  of  pH  3.0  and  Na  gelatinate  of  pH  10.0 
are  kept  in  solution  is  not  altered  as  long  as  not  too  much  of  the 
water  is  replaced  by  alcohol,  since  in  this  case  (NH4)2SO4  is 
always  a  better  precipitant  than  CaCl2  for  both  gelatin  chloride 
and  Na  gelatinate.  When,  however,  the  relative  amount  of 
alcohol  exceeds  a  certain  critical  point,  the  mechanism  by  which 
the  particles  of  gelatin  are  held  in  solution  changes  abruptly  as  is 
indicated  by  two  facts;  namely,  first  that  the  concentration  of  the 
salt  required  for  precipitation  becomes  suddenly  very  small,  and 
second,  that  the  efficient  ion  has  now  the  opposite  sign  of  charge  to 
that  of  the  colloidal  particle.  Thus,  in  the  case  of  gelatin  chloride 
(Table  XL VI),  the  critical  points  for  CaCl2  and  NaCl  are  close 
together  while  the  critical  point  for  (NH4)2SO4  is  at  a  much  lower 
concentration  of  alcohol.  In  this  case  the  gelatin  ion  has  a 
positive  charge  and  the  precipitating  ion  on  the  alcohol  side  of 
the  critical  point  is  the  anion.  In  Table  XL VII  the  critical 
points  for  (NH4)2SO4  and  for  NaCl  are  close  together  while  the 
critical  point  for  CaCl2  lies  at  a  much  lower  concentration  of 
alcohol.  In  this  case  the  colloidal  ion  is  negatively  charged  and 
the  precipitating  ion  of  the  salt  is  the  cation.  The  valency  effect 
will  be  demonstrated  more  strikingly  in  a  later  part  of  this 
chapter. 

5.  If  the  precipitating  effect  of  low  concentrations  of  neutral 


256  THEORY  OF  COLLOIDAL  BEHAVIOR 

salts  on  colloidal  solutions  or  suspensions  is  the  result  of  the 
Donnan  equilibrium,  the  stability  of  such  solutions  must  be  due 
to  the  fact  that  when  isolated  protein  ions  are  beginning  to 
coalesce  a  Donnan  equilibrium  is  set  up  between  the  solution 
inside  each  nascent  micella  and  the  outside  solution,  which 
results  in  a  swelling  of  the  nascent  micella  whereby  the  ions  in  the 
process  of  coalescence  are  forced  apart  again.  This  prevents  the 
formation  of  new  micellae  from  protein  ions  as  well  as  the  coales- 
cence into  larger  complexes  of  the  micellae  already  existing.  More- 
over, there  must  also  originate  a  P.D.  between  the  micella  and 
the  solution,  and  the  mutual  repulsion  of  the  micellae  due  to  their 
electrification  will  also  prevent  the  coalescence  of  individual 
micellae  into  a  precipitate.  If  a  salt  is  added,  the  forces  guaran- 
teeing the  stability  of  the  colloidal  solution,  e.g.,  the  osmotic 
pressure,  swelling,  and  P.D.  of  the  micellae  are  diminished. 
When  these  forces  fall  below  a  certain  minimal  value  the  protein 
particles  will  coalesce. 

We  have  seen  that  the  depressing  effect  of  a  salt  on  swelling, 
osmotic  pressure,  and  P.D.  of  protein  particles  is  due  to  that  ion 
of  the  crystalloidal  salt  which  has  the  opposite  sign  of  charge  to 
that  of  the  protein  ion;  and  that  the  depressing  effect  of  this 
crystalloidal  ion  increases  with  its  valency.  Thus,  Fig.  76 
indicates  the  depressing  effect  of  different  concentrations  of  NaCl 
and  Na2SC>4  on  osmotic  pressure  and  P.D.  of  a  1  per  cent  gelatin 
chloride  solution  of  pH  of  originally  3.5.  The  abscissae  are  the 
concentration  of  the  salt  added,  the  ordinates  the  osmotic  pressure 
and  P.D.  The  figure  shows  that  the  depressing  effect  of  the  same 
molecular  concentration  of  Na2SO4  is  much  more  than  twice  as 
great  as  the  depressing  effect  of  NaCl.  If  we  assume  that  the 
protein  ions  and  protein  micellae  can  coalesce  when  the  osmotic 
pressure  is  100  mm.  and  the  P.D.  about  4  millivolts,  this  low 
osmotic  pressure  and  low  P.D.  of  the  1  per  cent  solution  of  gelatin 
chloride  of  pH  originally  3.5  will  be  produced  when  the  NaCl 
solution  is  about  M/64  and  the  Na2SO4  about  M/512.  The 
precipitating  effect  of  Na2SO4  on  gelatin  chloride  would  then  be 
about  eight  times  as  great  as  the  precipitating  effect  of  NaCl. 
The  depressing  effect  of  CaCl2  on  the  osmotic  pressure,  swelling, 
and  P.D.  is  about  the  same  as  that  of  a  NaCl  solution  of  the  same 
concentration  of  chlorine  ions,  showing  that  the  depressing  effect 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


257 


is  due  to  the  anion.  Hence,  the  precipitating  effect  of  CaCU  on 
gelatin  chloride  is  about  the  same  as  that  of  a  NaCl  solution  of 
the  same  concentration  of  Cl  ions. 

When  the  gelatin  ion  has  a  negative  charge,  e.g.,  in  the  case  of 
Na  gelatinate,  the  depressing  effect  of  neutral  salts  on  the  P.D., 
osmotic  pressure,  or  swelling  of  the  gelatin  solution  is  due  to  the 


4096  2048 IU2?  5IZ  256  125 

Concentration  of  salt  solution 

FIG.  76. — Depressing  effect  of  salts  (NaCl  and  Na2SO4)  on  P.D.  and  on  osmotic 
pressure  of  a  1  per  cent  gelatin  chloride  solution  of  pH  3.5. 

cation  of  the  neutral  salt  and  increases  rapidly  with  the  valency  of 
the  salt.  This  is  illustrated  in  Fig.  37,  p.  107,  which  expresses 
the  effect  of  neutral  salts  on  the  swelling  of  Na  gelatinate  of  a  pH 
of  about  9.3.  It  is  obvious  that  in  order  to  depress  the  original 
volume  of  the  Na  gelatinate  to  one-half  a  M/512  solution  of 
CaCl2  and  a  M/16  solution  of  NaCl  and  about  M/32  solution  of 
are  required.  In  other  words,  the  depressing  action  of 

17 


258  THEORY  OF  COLLOIDAL  BEHAVIOR 

CaCl2  on  the  swelling  of  Na  gelatinate  is  more  than  10  times 
as  great  as  that  of  NaCl.  While  these  data  are  only  semiquan- 
titative,  they  enable  us  to  form  an  approximate  estimate  as 
to  whether  or  not  the  precipitating  action  of  a  salt  on  gelatin 
can  be  due  to  a  diminution  of  the  osmotic  pressure  (or  P.D.) 
between  the  coalescent  ions  of  gelatin  in  conformity  with  the 
Donnan  equilibrium. 

The  procedure  in  our  experiments  was  as  follows :  A  stock  solu- 
tion of  5  per  cent  gelatin  chloride  of  pH  3.0  was  prepared;  2 
c.c.  of  this  solution  were  heated  to  about  45°C.  to  bring  about 
complete  liquefaction,  and  50  c.c.  of  absolute  alcohol  were  added 
while  the  gelatin  was  still  warm  and  liquid.  This  concentration 
of  alcohol  was  in  excess  of  that  required  for  the  critical  limit,  and 
the  gelatin  solution  was  slightly  opalescent.  Ten  cubic  centi- 
meters of  this  mixture  of  gelatin-alcohol-water  were  titrated  with 
different  salt  solutions  until  a  precipitate  was  found.  The  con- 
centration of  the  salt  solution  was  selected  in  such  a  way  that 
not  less  than  0.3  and  not  more  than  0.8  c.c.  of  solution  were 
required  for  precipitation  to  avoid  the  addition  of  too  large  a 
volume  of  water  to  the  solution.  The  difference  in  the  relative 
efficiency  of  the  different  electrolytes  is  therefore  expressed  chiefly 
in  the  concentration  of  the  solution  required  for  precipitation. 
The  reader  should  bear  in  mind  that  the  pH  of  the  gelatin  chloride 
solution  after  the  alcohol  and  the  salt  solution  were  added  could 
not  be  measured,  and  that  it  was  probably  higher  than  3.0  and 
about  the  same  in  all  solutions.  In  order  to  be  able  to  compare 
the  relative  flocculating  efficiency  of  different  salts  the  flocculat- 
ing concentration  is  expressed  in  equivalents  of  cubic  centimeters 
of  M/1,024. 

Table  XL VIII  shows  that  all  salts  with  monovalent  anion  have 
a  lower  flocculating  power  on  gelatin  chloride  than  salts  with 
divalent  anion. 

Salts  with  monovalent  anion  require  a  molecular  concentration 
of  about  100/1,024,  i.e.,  about  M/10  concentration  for  precipita- 
tion, while  those  of  the  second  group  require  a  molecular  concen- 
tration of  about  10/1,024,  i.e.,  about  M/100  or  less.  This  shows 
that  the  difference  in  the  flocculating  power  of  monovalent  and 
bivalent  anions  has  roughly  the  ratio  of  about  1:10,  i.e.,  that  it 
corresponds  to  the  ratio  to  be  expected  from  Fig.  70  within  the 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


259 


limits  of  the  accuracy  of  these  experiments,  which  is  not  very 
great. 

TABLE   XLVIII. — FLOCCULATING   CONCENTRATION   OF   DIFFERENT  SALTS 

AND    ACIDS    IN    AN    ALCOHOL-WATER    MIXTURE    OF    GELATIN    CHLORIDE 


Cubic 

Equivalent, 

Concentration 

Nature 

centimeters  of 

cubic 

of  salt  used 

of  salt 

salt  solution 

centimeters 

required 

M/1,024 

M/8 

RbCl 

0.8 

102.0 

M/8 

KC1 

0.8 

102.0 

M/8 

NaCl 

0.8 

102.0 

M/8 

LiCl 

0.7 

90.0 

M/8 

MgCl2 

0.5 

64.0 

M/8 

CaCl2 

0.65 

83.0 

M/8 

SrCl2 

0.60 

77.0 

M/4 

BaCl2 

0.5 

128.0 

M/8 

LaCl3 

0.7 

90.0 

M/2 

CeCl3 

0.35 

179.0 

M/2 

A1C1, 

0.3 

153.0 

M/4 

HC1 

0.4 

102.0 

M/8 

NaBr 

0.8 

102.0 

M/4 

HBr 

..      0.3 

77.0 

M/8 

Nal 

0.6 

77.0 

M/8 

NaNO3 

0.7 

90.0 

M/4 

HN03 

0.3 

77.0 

M/8 

NaCNS 

0.4 

51.0 

M/128 

Na2SO4 

0.8 

6.4 

M/32 

H2SO4 

0.35 

11.2 

M/64 

Na2  oxalate 

0.65 

10.4 

M/128 

Na3  citrate 

0.7 

5.6 

M/128 

•    Na4Fe(CN)6 

0.4 

3.2 

It  was  almost  impossible  to  cause  flocculation  with  acetic  acid, 
oxalic  acid,  or  tartaric  acid.  This  suggests  that  secondary 
valency  forces  may  play  some  role. 

These  experiments  then  show  that  the  relative  efficiency  of 
Na2SO4  and  NaCl  for  the  flocculation  of  gelatin  chloride  in 
alcohol-water  solution  is  apparently  of  about  the  same  order 
of  magnitude  as  their  relative  efficiency  for  the  depression  of  the 
osmotic  pressure  of  gelatin  solutions. 


260 


THEORY  OF  COLLOIDAL  BEHAVIOR 


Table  XLIX  shows  the  relative  flocculating  efficiency  of 
cations  on  alcoholic  solutions  of  Na  gelatinate.  Ten  cubic 
centimeters  of  1  per  cent  Na  gelatinate  of  pH  10.0  were  mixed 
with  50  c.c.  of  absolute  alcohol.  The  mixture  is  slightly  opales- 
cent. Ten  cubic  centimeters  of  the  mixture  were  titrated  with 
various  salt  solutions  until  precipitation  occurred. 


TABLE  XLIX. — FLOCCULATING  CONCENTRATION  OF  DIFFERENT  SALTS  AND 
ALKALIES  IN  AN  ALCOHOL-WATER  MIXTURE  OF  Na  GELATINATE 


Cubic 

Equivalent, 

Concentration 

Nature  of  salt 

centimeters 

cubic 

used 

or  alkali 

of  solution 

centimeters 

required 

M/1,024 

M/16 

NaCl 

0.6 

38.4 

M/16 

NaBr 

0.6 

38.4 

M/16 

Nal 

0.45 

29.0 

M/16 

NaNO3 

0.5 

32.0 

M/16 

NaCNS 

0.55 

35.0 

M/16 

Na2S04 

0.75 

48.0 

M/16 

Na2  oxalate 

0.6 

38.4 

M/16 

Na$  citrate 

0.6 

38.4 

M/32 

Na4Fe(CN)6 

0.8 

25.6 

M/16 

KC1 

0.5 

32.0 

M/16 

LiCl 

0.6 

38.4 

M/4 

KOH 

0.3 

77.0 

M/4 

NaOH 

0.35 

90.0 

M/256 

MgCl2 

0.55 

2.2 

M/512 

CaCl2 

0.85 

1.7 

M/512 

SrCl2 

0.8 

1.6 

M/512 

BaCl2 

0.65 

1.3 

M/512 

LaCl3 

0.6 

1.2 

M/512 

CeCl3 

0.7 

1.4 

M/200 

Ca(OH)2 

1.0 

5.1 

M/100 

Ba(OH)2 

0.9 

9.2 

There  are  again  two  distinct  groups,  this  time  according  to  the 
valency  of  the  cation.     All  electrolytes  with  monovalent  cation 

40  1 

require  a  molecular  concentration  of  almost  .,       .    =        and  all 

l, 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  261 

salts  with  a  cation  of  higher  valency  a  concentration  of  almost 
M/500. 

We,  therefore,  find  that  for  the  flocculation  of  Na  gelatinate, 
originally  of  pH  10.0,  salts  with  bivalent  cation  are  about  20 
times  as  efficient  as  salts  with  monovalent  cation.  This  is 
roughly  in  harmony  with  the  relative  influence  of  these  ions  on 
the  osmotic  pressure  of  solutions  of  Na  gelatinate,  where  the 
efficiency  of  a  M/ 16  solution  of  NaCl  is  equaled  by  that  of  a  M/512 
solution  of  CaCl2  (Fig.  37). 

Schulze,  Linder  and  Picton,  and  Hardy  found  that  the  precipi- 
tating ion  has  the  opposite  sign  of  charge  to  that  of  the  colloidal 
particle  and  that  the  precipitating  efficiency  of  the  ion  increases 
with  its  valency.  These  experiments  suggest  that  the  rule  of 
Schulze,  Linder  and  Picton,  and  Hardy  is  only  a  consequence 
of  the  Donnan  equilibrium. 

6.  If  the  osmotic  pressure  set  up  between  coalescing  protein 
ions  is  able  to  prevent  the  formation  of  new  micellae  and  thus  to 
contribute  towards  the  stabilization  of  a  solution  of  gelatin  in  a 
solution  of  much  alcohol  and  little  water,  we  can  predict  another 
result  which  will  become  clear  from  Fig.  77.  This  figure  repre- 
sents the  influence  of  different  concentrations  of  NaCl  on  the 
osmotic  pressure  of  1  per  cent  solutions  of  originally  isoelectric 
gelatin  brought  to  pH  1.8,  4.1,  and  3.1  by  the  addition  of  different 
quantities  of  HC1.  It  is  obvious  from  the  curves  that  it  requires 
a  higher  concentration  of  NaCl  to  bring  the  osmotic  pressure  of 
the  gelatin  chloride  solution  to  the  same  low  value,  e.g.,  125  mm., 
when  the  pH  is  3.1  than  when  it  is  4.1.  At  pH  3.1  the  concen- 
tration of  NaCl  must  be  between  M/64  and  M/128  and  at  pH 
4.1  the  concentration  can  be  less  than  M/512.  At  pH  1.8  no 
addition  of  salt  is  required  since  the  osmotic  pressure  is  already 
below  125  mm.  If  it  be  true  that  the  difference  of  osmotic 
pressure  between  the  inside  of  the  nascent  micellae  and  the  sur- 
rounding solution  is  one  of  the  forces  guaranteeing  the  stability 
of  the  solution  of  gelatin  in  an  alcohol-water  mixture  when  the 
critical  limit  of  alcohol  is  exceeded,  it  is  obvious  that  the  con- 
centration of  salt  required  for  flocculation  should  vary  with  the 
original  pH  of  the  gelatin  solution  in  the  way  characteristic  for 
the  Donnan  equilibrium,  namely  that  near  the  isoelectric  point 
little  or  no  salt  should  be  required  for  precipitation,  that  with 


262 


THEORY  OF  COLLOIDAL'  BEHAVIOR 


increasing  hydrogen  ion  concentration  (i.e.  increasing  addition  of 
HC1)  the  concentration  of  NaCl  required  for  flocculation  should 
first  increase  and  later — after  a  certain  pH — diminish.  We 
will  show  that  this  is  the  case. 


to 
0 


pH 


1.6 


\ 


450 
425 
400 
375 
350 
325 

30° 
275 

250 
225 

200 

1T5 
150 

125 

100 

75 

50 

25 

0 


)24  512  256  128 

Concentration  of  NaCl 

FIG.  77. — Difference  in  the  depressing  action  of  NaCl  solutions  on  the  osmotic 
pressure  of  gelatin  chloride  solution  of  different  pH. 

Ten  cubic  centimeters  of  a  5  per  cent  stock  solution  of  iso- 
electric  gelatin  containing  various  amounts  of  HC1  were  brought 
to  about  45°C.  and  40  c.c.  of  absolute  ethyl  alcohol  were  added. 


N,  r^ 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


263 


This  was  a  quantity  of  alcohol  in  excess 
of  that  required  to  bring  the  solution 
to  the  critical  point.  After  cooling  to 
room  temperature,  the  50c.c.  of  alcohol- 
water  solution  of  1  per  cent  originally 
isoelectric  gelatin  were  titrated  with  a 
2>^  M  NaCl  or  2J^  M  CaCl2  solution 
until  permanent  flocculation  occurred. 
The  number  of  cubic  centimeters  of  2^ 
M  NaCl  and  CaCl2  required  varied  with 
the  pH  of  the  original  gelatin  solution  as 
Table  L  indicates.  The  pH  in  the  table 
are  those  which  the  solution  of  gelatin 
would  have  had  if  it  had  been  diluted 
with  40  c.c.  of  water  instead  of  with 
alcohol.  We  do  not  know  the  actual  pH 
in  the  alcoholic  solutions  except  that  it 
should  be  less  than  without  alcohol. 

Near  the  isoelectric  point  and  in  fact 
up  to  about  pH  4.0  or  3.8  of  the  pH 
which  would  have  been  found  had  the 
solution  contained  no  alcohol,  the 
gelatin  was  not  completely  dissolved 
even  when  no  salt  was  added,  and  the 
same  was  true  when  the  pH  (in  our 
arbitrary  standard)  fell  below  1.6. 
From  pH  3.8  to  pH  2.4  the  cubic 
centimeters  of  2J^  M  NaCl  required 
for  flocculation  increased  from  0.03  c.c. 
atpH  3.8  to  1.3  c.c.  at  pH  2.4;  from 
then  on  it  diminished  again.  Since 
the  pH  in  the  alcoholic  solution  was 
probably  less  than  it  would  have  been 
in  a  solution  free  from  alcohol,  the 
maximal  stability  of  the  gelatin  in  an 
alcohol-water  mixture  was  at  a  pH 
greater  than  2.4.  These  results  are 
difficult  to  explain  on  any  other  basis 
than  the  Donnan  equilibrium. 


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264  THEORY  OF  COLLOIDAL  BEHAVIOR 

We  conclude  from  these  experiments  that  gelatin  forms  a 
colloidal  suspension  in  a  mixture  with  much  alcohol  and  little 
water  and  that  the  stability  of  the  suspension  depends  in  this 
case  upon  the  forces  set  up  by  the  Donnan  equilibrium  between 
the  micellae  and  the  surrounding  liquid,  these  forces  being  osmotic 
pressure  and  P.D. 

In  aqueous  solutions  or  in  solutions  with  little  alcohol  and  much 
water  the  stability  of  the  gelatin  solution  depends  on  forces  which 
have  no  connection  with  the  Donnan  equilibrium  and  which  may 
be  the  forces  of  secondary  valency  between  gelatin  ions  or  mole- 
cules and  the  molecules  of  water  which  are  supposed  to  be  respon- 
sible for  the  stability  of  crystalloidal  solutions  in  general. 

These  forces  of  secondary  valency  do  not  cease  to  exist  (though 
they  are  weak)  in  solutions  with  much  alcohol  and  little  water, 
and  these  forces  may  contribute  also  to  the  stability  of  the  solu- 
tion. This  seems  to  be  indicated  by  some  of  the  data  in  Table 
XL VIII.  This  table  shows  that  M/10  NaCl  precipitates  gelatin 
from  the  solution  in  much  alcohol  and  little  water.  If  the  forces 
due  to  the  Donnan  equilibrium  alone  determine  the  stability  of 
the  suspension,  a  M/20  CaCl2  solution  and  a  M/30  LaCl3  solution 
should  have  the  same  effect,  since  only  the  anion  acts  in  the  case 
of  the  Donnan  effect  when  gelatin  is  positively  charged.  Table 
XL VIII  shows  that  the  CaCl2  and  LaCls  solutions  required  for 
precipitation  are  higher  than  M/20  or  M/30,  namely  M/12  for 
CaCl2  and  M/ll  for  LaCla.  This  means  that  Ca  and  still  more 
La  have  an  inhibiting  effect  on  the  precipitation.  We  have  seen 
that  Ca  and  La  increase  the  solubility  of  isoelectric  gelatin  in 
water,  i.e.,  they  increase  the  forces  of  attraction  between  water 
and  gelatin  (see  Table  XL VIII).  It  is  possible  that  the  inhibition 
of  the  precipitating  effect  of  Cl  by  La  and  Ca  is  due  to  the 
augmenting  effect  of  these  cations  on  the  solubility  of  gelatin  in 
water.  This  inhibiting  effect  on  precipitation  is  often  spoken  of 
as  the  peptization  effect.  While  the  precipitating  effect  is  due  to 
the  action  of  salts  on  the  Donnan  equilibrium,  the  peptization 
effect  seems  to  be  due  to  the  influence  of  salts  on  the  secondary 
valency  forces  between  molecules  of  gelatin  and  solvent,  in  these 
experiments  at  least. 

A  few  remarks  may  be  added  concerning  the  precipitation  of 
crystalline  egg  albumin  from  aqueous  solutions  by  salts  at  room 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  265 

temperature.  While  the  precipitation  of  solutions  of  sodium 
alburninate  and  of  isoelectric  albumin  requires  enormous  con- 
centrations of  salts,  the  precipitation  of  solutions  of  albumin 
chloride  of  pH  2.0  or  below  is  brought  about  by  salt  solutions  of 
much  lower  concentrations  (e.g.,  M/2  NaCl,  M/4  MgCl2,  etc.). 
This  is,  perhaps,  connected  with  the  fact  that  solutions  of  albumin 
chloride  become  opalescent  at  high  hydrogen  ion  concentrations, 
and,  therefore,  assume  more  the  character  of  suspensions. 

The  precipitation  of  albumin  chloride  by  salts,  from  solutions 
in  much  alcohol  and  little  water,  gives  results  similar  to  those 
reported  for  the  precipitation  of  gelatin  chloride  from  solutions 
in  much  alcohol  and  little  water.  The  inhibiting  action  of  the 
divalent  and  trivalent  cations  was  also  observed  in  the  case  of 
the  precipitation  of  albumin  chloride  from  alcoholic  solutions. 
The  precipitation  of  Na  alburninate  by  salts,  from  solutions  in 
much  alcohol  and  little  water,  gives  results  similar  to  those 
reported  for  the  precipitation  of  Na  gelatinate  from  solutions  in 
much  alcohol  and  little  water.  The  alcoholic  albumin  solutions 
used  were  slightly  opalescent,  or  in  other  words,  they  were  no 
longer  solutions  but  primarily  suspensions  of  micellae. 


CHAPTER  XV 
THE  STABILITY  OF  PROTEIN  SOLUTIONS  (Continued) 

B.  THE  STABILITY  OF  SOLUTIONS  OF  CASEIN  IN  WATER1 

Since  isoelectric  casein  is  practically  insoluble  in  water  it  is 
easy  to  study  the  mechanism  of  solution  of  granules  of  casein  in 
aqueous  solutions  of  acid  and  alkali.  When  this  is  done  it  is 
found  that  this  mechanism  is  entirely  different  in  the  two  media. 
In  an  alkaline  solution,  e.g.,  NaOH,  casein  granules  dissolve  very 
much  as  do  particles  of  sodium  oleate,  the  solution  of  which  is 
accompanied  by  phenomena  of  spreading.  According  to  Quincke 
such  phenomena  of  spreading  are  due  to  a  sudden  lowering  of 
surface  tension  between  the  surface  layer  of  soap  and  water, 
whereby  projecting  small  particles  of  the  surface  are  torn  off  so 
that  the  surface  of  the  granules  soon  becomes  smooth.  This 
happens  in  the  case  of  casein  granules  in  alkali.  There  is  no 
swelling  noticeable  in  the  particle. 

The  forces  which  drive  the  Na  caseinate  into  solution  are  not 
the  forces  of  the  Donnan  equilibrium.  If  this  were  the  case  the 
rate  of  solution  of  the  granules  should  reach  a  maximum  at  a 
pH  of  between  10.0  and  12.0  and  should  then  diminish.  As  a 
matter  of  fact  the  rapidity  of  solution  increases  indefinitely  with 
the  pH  of  the  NaOH.  In  M/2  NaOH  the  solution  of  the  granule 
occurs  almost  instantaneously.  This  agrees  with  the  fact  that 
solutions  of  Na  caseinate  in  water  require  very  high  concentra- 
tions of  NaCl  or  LiCl  or  NH4C1  for  precipitation. 

A  Na  caseinate  solution  of  pH  7.0  was  prepared  containing 
2  gm.  of  originally  isoelectric  casein  in  100  c.c.  solution.  Five 
cubic  centimeters  of  this  solution  were  added  to  5  c.c.  of  solutions 
of  different  salts  also  of  pH  7.0.  No  precipitation  was  observed 
when  the  concentration  of  NaCl  in  the  caseinate  solution  was 
M  or  that  of  LiCl  was  3>^  M,  or  that  of  NH4C1  was  2  M. 


1  LOEB,  J.,  and  LOEB,  R.  F.,  J.  Gen.  Physiol.,  vol.  4,  p.  187,  1921-22. 

266 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  267 

Precipitation  occurred  in  (NH^SCK  when  the  concentration  of 
this  salt  in  the  casein  solution  was  2  M.  Precipitation  occurred 
in  low  concentrations  of  CaCl2,  namely  M/128.  In  this  latter 
respect  the  solution  of  Na  caseinate  differed  from  a  solution  of 
Na  gelatinate  in  water.  The  facts  indicate  that  the  stability  of 
a  solution  of  Na  caseinate  in  water  is  not  due  to  a  Donnan 
equilibrium. 

It  can  be  shown  that  the  solution  of  granules  of  isoelectric 
casein  in  HC1  depends  on  forces  regulated  by  the  Donnan  equi- 
librium and  that  the  rule  of  Hardy  is  only  a  consequence  of  this 
fact.  This  can  be  proven  by  microscopic  observation  of  the 
mechanism  of  the  solution  of  solid  particles  of  originally  isoelectric 
casein  in  solutions  of  acids  of  different  concentration.  It  was 
found  that  the  particles  of  casein  swell  in  a  solution  of  HC1, 
becoming  more  and  more  transparent  the  more  they  swell,  and 
that  when  the  swelling  has  reached  a  certain  stage,  the  particles 
disappear — they  are  dissolved.  When  in  the  swollen  stage, 
slight  agitation  may  make  them  fall  apart.  T.  B.  Robertson 
had  suggested  such  a  mechanism  for  the  solution  t)f  Na  caseinate, 
but  we  have  seen  that  the  mechanism  of  solution  in  this  latter 
case  is  different.  There  is  no  doubt,  however,  that  the  swelling 
of  casein  particles  is  a  necessary  prerequisite  for  the  solution  of 
casein-acid  salts,  since  such  particles  are  only  dissolved  when 
their  swelling  exceeds  a  definite  limit. 

The  method  of  procedure  was  as  follows:  A  small  number  of 
granules  of  isoelectric  casein  of  the  same  size  (going  through  a 
sieve  with  mesh  100  but  not  through  a  sieve  with  mesh  120) 
were  put  into  50  c.c.  of  water  containing  different  quantities  of 
different  acids  and  kept  at  24°C.  At  various  intervals,  i.e., 
after  15,  and  60  minutes,  and  6,  and  24  hours,  the  diameter  of 
about  15  grains  was  measured  with  a  micrometer  under  a  micro- 
scope and  the  average  diameter  calculated.  The  particles  were 
not  stirred,  and  care  was  taken  to  avoid  their  breaking  into 
smaller  fragments.  The  averages  after  1  hour  are  plotted  in 
Fig.  78.  The  abscissae  are  the  logarithms  of  the  concentrations 
of  acid  of  the  aqueous  solution,  the  ordinates  are  the  average 
diameters  of  the  particles.  It  is  obvious  that  the  average 
diameter  of  the  particles  increases  at  first  with  the  increase  of 
the  concentration  of  the  acid,  reaching  a  maximum  at  about  pH 


268 


THEORY  OF  COLLOIDAL  BEHAVIOR 


2.0  of  the  outside  solution,  and  with  a  further  increase  in  the 
concentration  of  the  acid  the  swelling  becomes  less  again. 

Figure  79  gives  the  measurements  of  the  same  particles  after 
24  hours.  At  this  time  all  the  particles  in  the  region  of  greatest 
solubility  for  HC1  and  for  H3PO4,  i.e.,  between  pH  of  the  outside 


Swelling  of  casein 
in  different  acids 
at  24°  C  in  1  hour 


Concentration  of  acids 

FIG.  78. — Influence  of  different  acids  on  the  swelling  of  casein. 

solution  of  1.8  and  2.9,  had  completely  dissolved  and  could  no 
longer  be  measured. 

Figure  79  shows  another  fact;  namely,  that  the  rate  of  swelling 
is  not  the  same  in  different  acids.  It  is  about  the  same  inHCl 
and  H3PO4  (for  the  same  pH)  but  decidedly  less  in  HNO3  and 
still  less  in  H2SO4  and  trichloracetic  acid.  It  was  found  that  the 
rate  of  solution  of  casein  in  these  different  acids  followed  closely 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


269 


the  rate  of  swelling.  It  took  longer  to  dissolve  casein  in  HNO3 
than  it  did  in  HC1  (at  20°C.);  and  the  casein  was  practically 
insoluble  in  H2SC>4  and  trichloracetic  acid  in  24  hours. 

The  rate  of  swelling  is  a  function  apparently  not  only  of  the 
osmotic  pressure  inside  the  particle  caused  by  the  Donnan  equilib- 


2.5 

N    H     H    H 
lOOD  500     200    100 

Concentration  of  acids 

Fio.  79. — Connection  between  swelling  and  solution  of  casein  particles. 

rium,  but  also  of  the  force  of  cohesion  between  the  particles. 
Procter  and  Wilson  have  suggested  that  the  rapid  increase  of 
swelling  of  solid  gelatin  with  a  rise  in  temperature  is  due  to  a 
corresponding  diminution  of  cohesion  between  the  molecules  of 
gelatin  with  rising  temperature.  The  influence  of  the  anionof 
gelatin-acid  salts  on  the  cohesion  of  the  particles  of  a  solid  gel  is 
apparently  much  smaller  than  the  influence  of  the  anion  on  the 


270 


THEORY  OF  COLLOIDAL  BEHAVIOR 


cohesion  of  particles  of  casein-acid  salts.  The  forces  of  cohesion 
in  the  case  of  casein  sulphate  and  casein  trichloracetate  seem  to  be 
so  great  that  they  cannot  be  overcome  by  the  osmotic  pressure 
due  to  the  Donnan  equilibrium;  and  hence,  no  swelling  (and  as  a 
consequence  no  solution)  of  solid  casein  is  possible  in  H2SO4  or 
trichloracetic  acid.  The  influence  of  valency  on  the  Donnan 
equilibrium  is  the  same  in  the  case  of  the  swelling  of  casein  and  of 


5.5 


5.0 


4.5 


4.0 


3.5 


3.0 


X 


Depressing  effect  of 
NaCl  on  swelling 
and  solution  of 
casein  in   acid 


\ 


1524 

Concentration  of  NaCl 


I 


FIG.  80.  —  Depressing  action  of  NaCl  on  swelling  and  solution  of  casein  in  acid. 

gelatin;  what  is  different  is  the  influence  of  certain  ions  on  the 
relative  affinity  of  casein  ions  for  water  and  for  each  other. 

Procter  and  Wilson  have  shown  that  the  theory  of  the  Donnan 
equilibrium  explains  the  depressing  effect  of  a  salt  on  the  swelling 
of  solid  gelatin.  Microscopic  measurements  of  the  influence  of 
NaCl  on  the  rate  of  swelling  of  individual  grains  of  casein  particles 
in  M/100  HC1  were  made  at  24°C.,  and  the  results  plotted  in 


THE  STABILITY  OF  PROTEIN  SOLUTIONS 


271 


Fig.  80.  The  ordinates  are  the  average 
diameters  of  the  particles  after  1  and  24  hours 
respectively.  The  abscissae  are  the  concentra- 
tions of  NaCl.  The  depressing  effect  is 
similar  to  that  found  in  the  case  of  the  swell- 
ing of  a  jelly  of  gelatin.  After  24  hours  the 
particles  had  dissolved  in  the  NaCl  solutions 
of  a  concentration  below  M/256,  but  not  in 
concentrations  of  NaCl  higher  than  M/256. 

That  the  solution  of  casein  chloride  is  thus 
regulated  to  a  large  extent  by  the  Donnan 
effect  was  ascertained  also  by  measurements 
of  the  quantity  of  casein  chloride  dissolved 
at  20°C.  at  various  pH  of  the  solution.  One 
gram  of  isoelectric  powdered  casein  was  put 
into  100  c.c.  of  solutions  of  HC1  of  different 
concentration  and  kept  in  these  solutions  in 
one  case  for  1  hour,  in  a  second  case  for  22 
hours.  The  mass  was  then  poured  into  grad- 
uated cylinders  and  the  undissolved  part  was 
allowed  to  settle  to  the  bottom  for  2  and  for 
6  hours  respectively  at  20°C.  The  super- 
natant liquid  was  removed  and  the  sediment 
dried  over  night  in  an  oven  at  about  100°C. 
Table  LI  gives  the  result.  The  dry  weight 
of  1  gm.  of  isoelectric  casein  was  found  to  be 
0.870  gm.  and  this  weight  diminished  by  the 
dry  weight  of  the  sediment  was  the  amount 
dissolved.  Table  LI  shows  that  the  rate  of 
solution  increases  with  diminishing  pH  from 
4.36  to  2.18  where  the  solubility  of  casein 
chloride  is  a  maximum ;  with  a  further  decline 
in  pH  the  solubility  diminishes  again.  This 
is  in  agreement  with  the  Donnan  effect. 

In  a  similar  way  the  depressing  effect  of 
NaCl  on  the  rate  of  solution  of  casein 
chloride  was  ascertained  (Fig.  80).  Solutions 
of  12.5  c.c.  of  0.1  N  HC1  in  100  c.c.  and 
containing  1  gm.  of  powdered,  originally 


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272 


THEORY  OF  COLLOIDAL  BEHAVIOR 


isoelectric  casein  were  prepared  in  0,  M/2,048,  M/ 1,024,  to 
M/4  NaCl.  The  pH  of  a  solution  of  1  gm.  of  casein  in  100  c.c. 
containing  12.5  c.c.  of  0.1  N  HC1  was  2.12  and  this  pH  was  the 
same  in  all  solutions  made  up  in  NaCl.  The  solution  was  kept 
at  20°C.  for  16  hours  and  then  allowed  to  settle  for  24  hours  at 
20°  in  100  c.c.  graduated  cylinders.  The  dry  weight  of  the  sedi- 
ment was  determined  and  this  weight  when  deducted  from  the  dry 
weight  of  1  gm.  isoelectric  casein,  namely,  0.870  gm.,  was  the 
amount  that  had  gone  into  solution  after  a  correction  was  made 
for  the  free  NaCl  held  in  2  c.c.  solution  which  was  arbitrarily 
assumed  not  to  have  been  removed.  Though  this  latter  correc- 
tion was  somewhat  arbitrary,  it  could  have  caused  a  noticeable 
error  only  when  the  concentration  of  the  salt  solution  exceeded 
M/64.  For  the  solutions  of  M/64  and  below  this  error  was 
negligible.  Table  LII  gives  the  number  of  milligrams  of  casein 
which  had  gone  into  solution. 

TABLE  LII 


Concentration  of  NaCl 

M/2,048 

M/1,024 

M/512 

M/256 

M/128 

M/64 

Milligrams  dis- 
solved   

714 

685 

665 

615 

449 

282 

The  main  fact  is  that  a  slight  increase  in  the  concentration  of 
NaCl  causes  a  noticeable  drop  in  the  rate  of  solution.  Thus, 
M/1,024  NaCl  causes  a  noticeable  diminution  in  the  solubility 
of  a  1  per  cent  solution  of  casein  chloride  of  pH  2.12  at  24°. 

These  observations  then  indicate  that  the  solution  of  solid 
particles  of  casein  chloride  is  brought  about  by  the  ultimate 
elements  being  forced  apart  mechanically  through  the  process  of 
swelling.  The  force  acting  in  this  swelling  is  the  hydrostatic 
pressure  of  the  water  which  is  forced  into  the  interstices  of  the 
solid  particles  by  the  osmotic  pressure  of  the  solution  in  the 
interstices  between  the  casein  ions.  Procter  and  Wilson  have 
shown  that  the  application  of  Donnan's  theory  of  membrane 
equilibrium  accounts  quantitatively  for  this  swelling  on  the 
assumption  that  swelling  is  caused  by  the  excess  of  the  osmotic 
pressure  inside  the  gel  over  that  of  the  surrounding  solution 


THE  STABILITY  OF  PROTEIN  SOLUTIONS  273 

(Chap.  XI).  As  soon  as  the  osmotic  pressure  in  the  particle 
exceeds  the  forces  of  cohesion  between  the  casein  ions  of  the 
particle,  the  casein  ions  constituting  the  particle  are  separated. 

The  question  then  arises,  How  can  the  Donnan  effect  stabilize 
the  particles  of  casein  chloride  in  solution,  and  how  can  we  explain 
the  precipitating  effect  of  low  concentrations  of  neutral  salts? 
Let  us  assume  that  the  ultimate  particles  in  a  solution  of  casein 
chloride  of  pH  2.2  are,  (a)  isolated  casein  ions,  (6)  isolated  casein 
molecules,  and  (c)  small  casein  aggregates  or  micellae.  The 
Donnan  equilibrium  furnishes  two  kinds  of  forces  preventing 
that  degree  of  coalescence  of  these  particles  which  is  required  for 
precipitation;  namely,  the  osmotic  pressure  and  the  membrane 
potentials.  When  isolated  protein  ions  collide  and  remain 
attached  to  form  a  micella,  a  Donnan  equilibrium  is  established 
between  the  nascent  micella  and  the  surrounding  solution. 
The  Donnan  equilibrium  demands  that  there  be  a  higher  con- 
centration of  electrolytes  inside  than  outside  and  this  difference 
in  osmotic  pressure  leads  to  water  being  attracted  into  the  mi- 
cella. The  increase  in  hydrostatic  pressure  will  force  the  protein 
molecules  apart  again  and  thus  tends  to  prevent  the  formation 
of  the  micellae.  Moreover,  if  micellae  exist  in  the  casein  chloride 
solution  (aside  from  isolated  casein  ions  and  molecules)  the  coales- 
cence of  different  micellae  into  larger  aggregates  must  be  prevented 
by  the  potential  difference  between  the  micellae  and  the  surround- 
ing solution.  As  a  consequence  of  this  P.D.,  the  micellae  must 
repel  each  other.  This  charge  as  well  as  the  osmotic  pressure 
caused  by  the  Donnan  equilibrium  is  a  minimum  at  the  isoelectric 
point,  rises  rapidly  with  increasing  hydrogen  ion  concentration, 
reaching  a  maximum,  and  diminishes  again  with  a  further  increase 
in  hydrogen  ion  concentration  as  shown  in  a  preceding  chapter. 
The  osmotic  pressure  and  charge  are  also  diminished  by  the 
addition  of  salt.  In  this  case,  both  the  osmotic  pressure  as  well 
as  the  P.D.  are  depressed,  in  accordance  with  Donnan's  theory, 
and  when  this  depression  reaches  a  certain  degree  the  casein 
particles  coalesce.  They  will  also  aggregate  without  the  addition 
of  salt  at  or  near  the  isoelectric  point  where  these  forces  due  to 
the  Donnan  equilibrium  are  also  zero  or  sufficiently  low. 

These  conclusions  were  supported  by  experiments  on  the  pre- 
cipitation of  casein  chloride  solutions  by  salts.  The  concentra- 

18 


274  THEORY  OF  COLLOIDAL  BEHAVIOR 

tions  required  should  be  comparatively  low  and  this  was  found 
to  be  the  case.  One  per  cent  solutions  of  casein  chloride  of  pH 
2.2  were  prepared  in  different  concentrations  of  salts  in  water  of 
about  the  same  pH.  That  concentration  was  determined  which 
causes  an  almost  instantaneous  complete  precipitation  of  the 
protein  from  the  solution  so  that  the  supernatant  liquid  became 
as  clear  as  water.  These  concentrations  were  as  follows : 

NaCl about  M/8 

NaNO3 about  M/8 

CaCl2 about  M/8 

Na  trichloracetate about  M/16 

Na2SO4 about  M/32 

Though  the  results  are  only  semi-quantitative,  the  validity  of 
Hardy's  rule  and  the  valency  effect  are  easily  recognizable.  It 
is  also  obvious  that  the  concentrations  of  electrolytes  required 
for  instantaneous,  complete  precipitation  of  casein  chloride  are 
considerably  lower  than  those  required  for  the  precipitation  of 
Na  caseinate  from  their  watery  solution. 

Hardy's  rule,  that  only  that  ion  of  a  neutral  salt  is  active  in 
precipitation  which  has  the  opposite  sign  of  charge  to  that  of  the 
colloidal  ion,  and  that  the  efficiency  of  the  ion  increases  with  the 
valency,  is  simply  the  expression  of  the  Donnan  effect,  as  is  also 
the  fact  that  very  low  concentrations  of  electrolytes  suffice  for 
precipitation.  The  reader  will  notice  that  it  is  unnecessary  to 
assume  that  the  ions  are  adsorbed  by  the  casein  or  that  the  ad- 
sorption of  ions  annihilates  the  electrical  charges  on  the  particles 
of  casein. 


CHAPTER  XVII 

COLLOIDAL    SUBSTANCES,    COLLOIDAL    STATE,    AND 
COLLOIDAL  BEHAVIOR 

Graham  had  suggested  the  distinction  between  colloidal  and 
crystalloidal  substances,  but  it  was  found  later  that  one  and  the 
same  substance,  e.g.,  NaCl,"  may  behave  when  in  solution  either 
as  a  crystalloid  or  as  a  colloid.  It  then  was  proposed  to  drop  the 
distinction  between  colloidal  and  crystalloidal  substances  and  to 
distinguish  between  the  colloidal  and  the  crystalloidal  state  of 
matter.  The  reasons  are  summed  up  in  the  following  quotation 
from  Burton: 

" Modern  work  has  shown  that  it  is  incorrect  to  speak  of  colloidal 
substances  as  a  particular  class.  Krafft  has  observed  that  the  alkali 
salts  of  the  higher  fatty  acids — stearate,  palmitate,  oleate — dissolve 
in  alcohol  as  crystalloids  with  normal  molecular  weights,  but  in  water 
they  are  true  colloids.  The  reverse  is  true  of  sodium  chloride;  Paal 
found  that  the  latter  gave  a  colloidal  solution  in  benzol,  while,  of  course, 
it  gives  a  crystalloidal  solution  in  water  (Karczag).  More  recently, 
von  Weimarn  has  demonstrated,  by  the  preparation  of  colloidal  solu- 
tions of  over  two  hundred  chemical  substances  (salts,  elements,  etc.), 
that,  by  proper  manipulation,  almost  any  substance  which  exists  in 
the  solid  state  can  be  produced  in  solution,  either  as  a  colloid  or  as  a 
crystalloid;  and  that,  as  shown  by  many  other  workers,  in  some  cases 
it  is  merely  a  matter  of  the  concentration  of  the  reacting  components 
whether  one  gets  crystalloidal  or  colloidal  solutions. 

''Consequently,  we  now  speak  of  matter  being  in  the  colloidal  state 
rather  than  of  certain  substances  as  colloids — the  essential  character- 
istic of  the  colloidal  state  being  that  the  substance  will  exist  indefinitely 
as  a  suspension  of  solid  (or,  in  some  cases,  probably  liquid)  masses  of 
very  small  size  in  some  liquid  media,  e.g.,  water,  alcohol,  benzol,  gly- 
cerine, etc.  According  to  the  medium  employed  the  resulting  solutions 
or  suspensions  are  called,  after  Graham,  hydrosols,  alcosols,benzosols, 
glycersols,  etc."1 

1  BURTON,  E.  F.,  The  Physical  Properties  of  Colloidal  Solutions,  2d  ed., 
pp.  8-9,  London,  New  York,  Bombay,  Calcutta,  and  Madras,  1921. 

275 


276  THEORY  OF  COLLOIDAL  BEHAVIOR 

If  we  apply  the  conclusion  drawn  in  this  statement  to  the 
proteins,  it  follows  that  we  have  no  longer  any  right  to  insist 
that  proteins  can  form  only  colloidal  solutions.  If  solutions  of 
gelatin  and  of  crystalline  egg  albumin  behave  like  crystalloidal 
solutions  in  water  and  if  gelatin  solutions  in  alcohol  behave  like 
colloidal  solutions,  we  have  no  right  to  say  that  nevertheless 
albumin  and  gelatin  are  in  the  colloidal  state  when  dissolved  in 
water.  Such  an  assumption  is  as  arbitrary  as  to  say  that  NaCl 
is  in  a  colloidal  state  when  dissolved  in  water  simply  because  it 
is  in  a  colloidal  state  when  dissolved  in  benzol.  The  idea  that 
the  two  proteins  mentioned  must  be*  in  the  colloidal  state  when 
dissolved  in  water  is  a  survival  from  the  time  when  it  was  custom- 
ary to  discriminate  between  colloidal  and  crystalloidal  substances 
instead  of  between  colloidal  and  crystalloidal  states,  and  the 
terms  emulsoids  or  hydrophilic  colloids  when  applied  to  proteins 
which  require  high  concentrations  of  salt  for  their  precipitation 
are  also  a  survival  from  that  time.  The  fact  that  the  molecules 
of  protein  are  large  does  not  matter,  since  the  chemical  constitu- 
tion of  solute  and  solvent  and  not  the  mere  size  of  the  molecules  of 
solute  determines  the  stability  of  their  solution.  The  large  size 
introduces  only  interesting  complications  inasmuch  as  it  makes  it 
possible  that  one  and  the  same  molecule  may  have  groups  with  a 
different  degree  of  attraction  for  the  molecules  of  water  or  solvent. 

In  Burton's  statement  just  quoted  only  one  colloidal  property 
is  taken  into  consideration;  namely,  the  stability  of  colloidal 
solutions.  We  have  seen,  however,  that  as  far  as  the  proteins 
are  concerned  there  are  a  number  of  other  properties  of  colloidal 
solutions  which  are  all  as  characteristic  for  colloids  as  are  the 
conditions  for  the  stability  of  the  solutions;  and  that  as  a  matter 
of  fact  the  stability  of  colloidal  solutions  depends  on  these  other 
properties,  such  as  the  P.D.  and  the  osmotic  pressure.  It  is, 
therefore,  no  longer  possible  to  base  our  definition  of  colloids 
exclusively  on  data  derived  from  a  study  of  the  stability  of 
colloidal  solutions. 

The  general  characteristics  of  colloidal  behavior  may  be  stated 
as  follows : 

1.  Low  concentrations  of  neutral  salts  depress  the  osmotic 
pressure,  P.D.,  viscosity,  and  stability  of  colloidal  solutions  and 
the  swelling  of  gels. 


COLLOIDAL  SUBSTANCES  277 

2.  This  depressing  effect  of  the  salt  is  always  due  to  that  ion 
which  has  the  opposite  sign  of  charge  to  that  of  the  colloidal 
particle. 

3.  The  depressing  effect  increases  with  the  valency  of  the 
effective  ion. 

4.  When  the  colloidal  substance  used  is  an  amphoteric  electro- 
lyte the  addition  of  little  acid  or  alkali  to  the  isoelectric  substance 
increases  the  osmotic  pressure,  P.D.,  viscosity,  stability  of  the 
solution,  and  swelling  of  gel  until  a  point  is  reached  where  the 
further  addition  of  acid  or  alkali  will  have  the  opposite  effect. 

5.  The  depressing  effect  of  an  excess  of  acid  or  alkali  is  also  due 
to  the  ion  which  has  the  opposite  sign  of  charge  to  that  of  the 
colloidal  particle,  and  the  efficiency  of  that  ion  also  increases 
with  its  valency. 

It  is  obvious  that  the  stability  of  colloidal  solutions  is  only  one 
of  a  number  of  properties  which  all  possess  the  same  characteristic 
features.  It  has  been  shown  in  the  preceding  chapters  that 
all  these  characteristics  find  their  explanation  in  the  Donnan 
equilibrium. 

If,  on  the  basis  of  this  knowledge,  we  continue  the  mode  of 
reasoning  expressed  in  the  quotation  from  Burton,  we  come  to  the 
further  conclusion  that  it  is  no  longer  correct  to  discriminate 
between  the  colloidal  and  the  crystalloidal  state  of  matter,  for 
the  same  substance  may  behave  in  the  same  state  either  like  a 
colloid  or  a  crystalloid.  We  have  seen  that  a  1  per  cent  solution 
of  crystalline  egg  albumin  in  water  at  room  temperature  and  at  a 
pH  much  above  1.0  will  behave  like  a  colloid  or  as  if  it  were  in  the 
colloidal  state  in  regard  to  osmotic  pressure  or  in  regard  to  P.D. 
when  separated  from  water  by  a  collodion  membrane;  but  the 
same  solution  of  crystalline  egg  albumin  will  behave  like  a 
crystalloid  or  as  if  it  were  in  the  crystalloidal  state  in  regard  to 
the  stability  of  the  solution  and  practically  also  in  regard  to 
viscosity  (as  long  as  the  temperature  and  the  concentration  of 
the  solution  are  not  too  high  and  the  pH  not  too  low) .  The  reason 
for  this  is  plain  in  the  light  of  the  preceding  chapters.  Proteins 
(and,  perhaps,  substances  in  general)  will  show  colloidal  behavior 
when  the  following  two  conditions  are  fulfilled:  first,  the  sub- 
stance must  be  capable  of  dissociating  electrolytically,  and  second, 
one  of  the  two  oppositely  charged  ions  must  be  prevented  from 


278  THEORY  OF  COLLOIDAL  BEHAVIOR 

diffusing  while  the  other  is  free  to  diffuse.  In  this  case  a  Donnan 
equilibrium  is  established  resulting  in  an  unequal  distribution 
of  the  diffusible  ions  on  both  sides  of  the  membrane.  The 
forces  resulting  from  this  distribution  of  crystalloidal  ions  are 
the  only  cause  of  those  phenomena  which  are  designated  as 
colliodal. 

In  general  the  block  in  the  diffusion  of  one  kind  of  ions  can 
be  brought  about  by  two  kinds  of  conditions:  first,  by  mem- 
branes with  a  selective  permeability;  and,  second,  by  the  cohesion 
between  ions  of  one  kind.  An  electrolyte  which  exists  in  a  true 
solution  (and  this  is  in  all  probability  true  for  crystalline  egg 
albumin)  will  show  colloidal  behavior  in  regard  to  osmotic  pres- 
sure and  to  P.D.  when  separated  from  pure  water  by  a  membrane 
which  is  permeable  for  all  ions  in  the  solution  except  one.  More- 
over, when  ions  of  one  type  are  attracted  to  each  other  with 
greater  force  than  they  are  attracted  by  the  molecules  of  the 
solvent,  aggregates  are  formed,  and  when  these  aggregates  are 
permeable  to  other  ions  than  those  forming  the  aggregate,  a 
Donnan  equilibrium  is  also  established  and  colloidal  behavior 
follows  again.  This  latter  condition  leads  to  the  colloidal 
character  of  swelling,  viscosity,  and  of  the  stability  of  suspen- 
sions. Since  1  per  cent  solutions  of  crystalline  egg  albumin  are 
very  stable  at  room  temperature  and  as  long  as  the  pH  is  not  too 
low,  there  are  few  or  practically  no  aggregates  in  such  a  solution, 
and  the  crystalline  egg  albumin  behaves  in  regard  to  viscosity 
and  in  regard  to  the  stability  of  its  solutions  essentially  as  if  it 
were  in  the  crystalloidal  state.  Of  course,  the  proof  has  to  be 
furnished  that  crystalline  egg  albumin  exists  in  the  form  of 
isolated  molecules  in  agneous  solution.  S0rensen  has  calculated 
the  molecular  weight  of  crystalline  egg  albumin  from  measure- 
ments of  the  osmotic  pressure  of  this  substance  and  has  obtained 
results  which  make  this  conclusion  probable.1 

The  behavior  of  gelatin  is  especially  interesting.  Gelatin 
solutions  in  water  show  colloidal  behavior  in  regard  to  osmotic 
pressure  and  P.D.  when  the  solutions  are  separated  from  pure 
water  by  a  collodion  membrane  or  by  some  other  membrane  with 
similar  selective  permeability.  Gelatin  solutions  in  water  show 

1  S0RENSEN,  S.  P.  L.,  Studies  on  proteins:  Compt.  rend.  trav.  Lab,  Carlsberg, 
vol.  12,  Copenhagen,  1915-17. 


COLLOIDAL  SUBSTANCES  279 

also  colloidal  behavior  in  regard  to  viscosity  when  the  tempera- 
ture is  not  too  high,  and  this  is  due,  as  we  have  seen,  to  the  exist- 
ence in  such  solutions  of  submicroscopic  particles  of  gel  in  which 
the  diffusion  of  the  protein  ions  is  prevented  by  the  forces  of 
cohesion  between  the  protein  ions  forming  the  gel.  The  degree 
of  swelling,  and  the  relative  volume  occupied  by  these  particles 
in  the  solution  is  regulated  by  the  Donnan  equilibrium  and,  hence 
the  viscosity  of  a  gelatin  solution  is  also  regulated  by  the  Donnan 
equilibrium ;  in  other  words,  the  viscosity  of  gelatin  solutions  has 
the  peculiarities  of  colloidal  behavior.  Only  in  one  respect  do 
the  aqueous  solutions  of  gelatin  behave  as  if  gelatin  were  in  the 
crystalloidal  state,  namely  in  respect  to  the  stability  of  solutions. 
It  requires  high  concentrations  of  salts  to  precipitate  gelatin 
from  its  aquoues  solutions  and  the  sign  of  charge  of  the  precipitat- 
ing ion  has  no  relation  to  the  sign  of  charge  of  the  protein  ion. 
Of  course,  it  remains  still  to  be  proved  that  gelatin  exists  in 
aqueous  solution  essentially  in  the  form  of  isolated  ions  or  molecules 
and  almost  exclusively  so  if  the  temperature  is  above  35°C.  This 
proof  can  only  be  furnished  if  the  calculations  of  the  molecular 
weight  from  osmotic  pressure  measurements  are  supported  by 
other  measurements,  especially  by  determinations  of  the  chemical 
constitution  of  the  gelatin  molecule.  Dakin's1  analysis  leads 
to  a  molecular  weight  which  is  quite  compatible  with  the  results 
from  the  osmotic  pressure  determinations  (see  Chap.  X). 

We  have  seen  that  solutions  of  gelatin  in  alcohol-water  mixtures 
behave  like  suspensions  inasmuch  as  they  can  be  precipitated 
by  low  concentrations  of  salt  and  inasmuch  as  the  precipitating 
ion  has  now  the  opposite  sign  of  charge  to  that  of  the  protein  ion. 
When  the  gelatin  solution  is  in  this  state,  it  differs  in  two  respects 
from  a  gelatin  solution  in  pure  water:  it  has  a  comparatively 
low  viscosity,  and  it  no  longer"  sets  to  a  gel.  It  is  also,  as  a  rule, 
opalescent.  The  change  in  viscosity  can  be  shown  in  the  follow- 
ing way.2 

To  1  gm.  of  isoelectric  gelatin  enough  HC1  is  added  so  that  in 
a  1  per  cent  solution  in  water  the  pH  would  be  about  3.0.  This 
gelatin  is  dissolved  in  mixtures  of  water  and  alcohol,  heated 
rapidly  to  45°C.,  and  cooled  rapidly  to  15°C.  The  time  of 

1  DAKIN,  H.  D.,  J.  Biol.  Chem.,  vol.  44,  p.  499,  1920. 

2  The  following  experiments  have  not  yet  been  published. 


280 


THEORY  OF  COLLOIDAL  BEHAVIOR 


outflow  through  a  viscometer  is  measured  immediately  at  15°C. 
As  a  control  the  time  of  outflow  at  15°C.  of  identical  water- 
alcohol  mixtures  but  containing  no  gelatin  is  also  measured.  The 
ratio  of  the  time  of  outflow  of  the  gelatin-water-alcohol  mixture 
to  that  of  the  water-alcohol  mixture  without  gelatin,  i.e., 
the  relative  viscosity  of  the  gelatin  solution,  is  given  in  Table 
LIII.  The  upper  horizontal  row  gives  the  relative  amount  of 
alcohol  in  per  cent,  the  second  row  the  appearance  of  the  solution, 
the  third  the  time  of  outflow  of  the  gelatin  solution  in  seconds, 
the  fourth  row  the  time  of  outflow  of  the  alcohol-water  mixture 
without  gelatin,  and  the  last  row  the  relative  viscosity  of  the 

TABLE  LIII. — INFLUENCE  OF  INCREASING  QUANTITIES  OF  ALCOHOL  ON  THE 

VISCOSITY  OF  A  1  PER  CENT  SOLUTION  OF  GELATIN  CHLORIDE  OF 

ORIGINALLY  pH  3.0 


Concentration  of  alcohol  in  per  cent 

0 

40 

70 

80 

85 

87.5 

90 

slightly 

very 

Appearance  of  solution  

clear 

opalescent 

opalescent 

opales  cent 

Time   of   outflow   of   gelatin 

solution  in  seconds  

207 

266 

506 

362 

229 

185 

163 

Time  of  outflow  of  alcohol  + 

water,  without  gelatin  

80 

233 

225 

194 

178 

168 

160 

Relative  viscosity  

2.590 

2.860 

2.250 

1.860 

1.286 

1.100 

1.020 

gelatin  solution.  It  is  obvious  that  the  viscosity  drops  sharply 
between  80  per  cent  and  85  per  cent  of  alcohol,  and  that  at  85 
per  cent,  where  the  solution  is  already  opalescent,  the  relative 
viscosity  is  only  1.286  and  only  1.1  for  87.5  per  cent  alcohol. 

In  a  second  experiment  the  same  solutions  were  prepared  but 
the  solutions  were  kept  for  2  days  in  a  thermostat  at  9°C.,  the 
mixtures  were  then  rapidly  brought  to  15°C.,  and  the  viscosities 
determined.  The  solution  containing  60  per  cent  of  alcohol  or 
less  had  set  to  a  jelly;  the  solution  containing  70  per  cent  was 
almost  solid,  but  the  solutions  containing  80  per  cent  or  more  were 
all  completely  liquid.  Their  relative  viscosity  was  measured 
(Table  LIV)  and  was  found  to  be  only  slightly  larger  than  at 
the  beginning,  when  the  solution  contained  85  per  cent  or  more 


COLLOIDAL  SUBSTANCES 


281 


alcohol,  while  the  viscosity  had  risen  considerably  when  the 
solution  contained  less  than  80  per  cent  alcohol. 

The  opalescence  of  the  alcoholic  solutions  indicates  the  pres- 
ence of  aggregates  of  gelatin,  but  since  the  relative  viscosity  of 
these  alcoholic  solutions  is  low  as  compared  with  the  viscosity  of 
solutions  of  gelatin  in  pure  water,  and  since  the  alcoholic  solutions 
no  longer  set  to  a  jelly,  the  micellae  in  the  watery  solution  and  in 
the  alcohol-water  mixture,  containing  80  per  cent  alcohol  or 
more,  must  be  different.  The  fact  that  the  viscosity  ratio  is 
low  in  the  opalescent  gelatin-alcohol  solutions  (which  no  longer 
can  set  to  a  jelly)  indicates  that  the  micellae  in  this  solution 

TABLE  LIV. — VISCOSITY  AT  15°C.  AFTER  THE  SOLUTION  HAD  BEEN  KEPT 
AT  9°C.  FOR  2  DAYS 


Concentration  of  alcohol 

80 
per  cent 

85 
per  cent 

90 
per  cent 

Appearance  of  solution 

slightly 
opalescent 

521.0 

194.0 

2.685 

opalescent 

247.0 

178.0 
1.390 

very 
opalescent 

180.0 

160.0 
1.125 

Time  of  outflow  of  gelatin  solution  in 
seconds 

Time     of     outflow     of     alcohol-water 
mixture  without  gelatin 

Relative  viscosity  of  gelatin  solution.  .  . 

occlude  less  water  than  the  micellae  formed  in  the  solutions  of 
gelatin  in  water  (or  in  water  with  not  too  much  alcohol) . 

This  is  in  harmony  with  the  assumption  (made  in  Chap. 
XIV)  that  the  forces  which  hold  gelatin  in  solution  in  pure 
water  or  in  water  with  little  alcohol,  are  different  from  those 
which  hold  the  gelatin  in  solution  when  the  critical  limit  for 
alcohol  has  been  exceeded.  In  aqueous  solutions  or  in  solutions 
with  much  water  and  little  alcohol  where  setting  of  gelatin  to  a 
jelly  is  possible,  the  molecules  or  ions  of  jelly  are  distributed 
evenly  in  the  solvent  probably  on  account  of  the  strong  forces 
of  residual  valency  between  solute  and  solvent.  The  large 
gelatin  molecules  can  adhere  to  each  other  only  through  those 


282  THEORY  OF  COLLOIDAL  BEHAVIOR 

groups  which  have  a  stronger  attraction  for  each  other  than  they 
have  for  the  solvent.  The  other  groups  adhere  strongly  to  the 
solvent,  and  hence  they  cannot  come  in  contact  with  each  other 
even  when  the  gelatin  sets  to  a  jelly.  When  a  1  per  cent  solution 
of  gelatin  sets  to  a  gel  the  distribution  of  the  gelatin  molecules 
in  the  solvent  undergoes  probably  no  profound  change.  What 
may  change  is,  perhaps,  the  orientation  of  the  gelatin  molecules 
or  ions  towards  each  other,  but  not  their  average  distance  from 
each  other.  When,  however,  too  much  alcohol  is  added,  i.e., 
when  the  solution  is  on  the  alcohol  side  of  the  critical  point,  the 
forces  of  attraction  between  gelatin  and  solvent  are  weakened 
to  such  an  extent  that  the  groups  which  were  formerly  attracted 
by  the  solvent  are  now  more  strongly  attracted  to  each  other  than 
they  are  to  the  molecules  of  solvent.  In  the  micellae  thus  formed 
the  protein  ions  or  molecules  are  in  much  closer  contact  than  they 
are  in  a  jelly,  and  hence  they  occlude  much  less  water  than  the 
micellae  formed  in  pure  water  or  in  mixtures  of  water  with  little 
alcohol.  The  latter  micellae  increase  the  viscosity  of  the  solution 
more  than  the  micellae  formed  in  an  excess  of  alcohol.  The  gelatin 
would  be  precipitated  in  the  latter  solutions  if  it  were  not  for  the 
fact  that  the  coalescence  of  the  protein  ions  and  molecules-  is 
prevented  by  the  forces  set  up  as  a  consequence  of  the  Donnan 
equilibrium,  namely,  forces  of  osmotic  pressure  and  of  P.D.,  as 
stated.  When,  however,  a  small  quantity  of  salt  is  added  the 
forces  set  up  by  the  Donnan  equilibrium  are  diminished  and 
nothing  now  prevents  the  forces  of  attraction  between  the 
gelatin  molecules  from  causing  the  separating  out  of  the  gelatin 
from  solution.  It  should  also  be  recalled  that  at  the  isoelectric 
point  not  only  the  P.D.  but  also  the  osmotic  pressure  of  protein 
solutions  is  a  minimum  and  that  salts  depress  the  osmotic  pres- 
sure as  well  as  the  P.D. 

The  fact  that  a  Donnan  equilibrium  is  established  between 
micellae  and  surrounding  liquid,  whereby  the  opposite  ions  of 
electrolytes  are  distributed  in  a  definite  way  between  the  two 
constituents,  makes  it  clear  why  in  the  case  of  precipitation  of 
colloids  some  of  the  precipitating  electrolyte  must  be  found  in  the 
precipitate,  and  that  there  can,  as  a  rule,  be  no  stoichiometric 
relation  between  the  quantity  of  salt  and  the  mass  of  protein  in 
the  precipitate. 


COLLOIDAL  SUBSTANCES  283 

We  can  form,  on  the  basis  of  what  has  been  said,  a  more 
definite  picture  of  the  difference  between  gel  formation  and  pre- 
cipitation. When  gelatin  is  dissolved  in  pure  water  or  in  much 
water  with  little  alcohol,  probably  only  one  of  the  groups  of  the 
gelatin  molecule  has  a  greater  affinity  for  other  like  groups 
than  for  the  molecules  of  water,  while  all  the  other  groups  of  the 
gelatin  molecules  have  much  stronger  affinities  for  water  than 
for  each  other.  Hence  in  this  state  the  gelatin  molecules  can 
form  networks  by  their  "oily"  group  (i.e.,  the  groups  with  little 
affinity  for  water),  the  "oily"  group  of  one  molecule  adhering  to 
an  "oily"  group  in  the  neighboring  molecule.  The  rest  of  the 
groups  of  these  molecules  must,  however,  remain  separated, 
since  their  "watery"  groups  (i.e.,  the  groups  with  strong  affinity 
for  water)  cannot  adhere  to  each  other.  The  result  is  a  network 
in  which  the  distribution  of  the  molecules  in  the  water  is  not 
disturbed,  since  the  forces  of  attraction  between  the  "watery" 
groups  of  the  protein  molecule  and  the  molecules  of  water  will 
prevent  the  molecules  of  gelatin  from  attracting  each  other 
except  at  the  one  "oily"  group.  Since  the  "watery"  groups 
prevail  in  bulk  over  the  oily  group  of  the  gelatin  molecule  or 
ion,  a  solid  network  or  a  gel  formation  results  instead  of  pre- 
cipitation. Under  these  conditions  we  observe  the  gel  form 
of  micellae.  In  a  solution  with  much  alcohol  and  little  water 
(i.e.,  on  the  alcohol  side  of  the  critical  point)  the  situation  becomes 
reversed.  The  forces  of  attraction  between  the  "watery" 
groups  and  the  solvent — which  is  now  mainly  alcohol — are  weak, 
and  since  they  form  the  bulk  of  the  gelatin  molecules  the  latter 
will  attract  each  other  in  many  points,  thus  causing  a  close  con- 
tact over  a  wide  area  and  this  gives  rise  to  the  precipitation  form 
of  the  micellae.  On  the  other  hand,  the  few  "oily"  groups  of  the 
gelatin  molecule  may  now  be  attracted  by  the  alcohol  and  this 
may  aid  in  stabilizing  the  solution;  but  at  the  best  these  forces 
must  be  weak. 

In  the  case  of  crystalline  egg  albumin  the  forces  of  attraction 
between  the  watery  group  and  the  molecules  of  water  are  very 
strong  and  the  mutual  attraction  of  the  oily  groups  for  each 
other  must  be  very  feeble,  since  no  gel  formation  occurs  at  ordin- 
ary temperature,  low  concentration,  or  a  pH  above  1.2.  When, 
however,  the  temperature  or  the  hydrogen  ion  concentration  is 


284  THEORY  OF  COLLOIDAL  BEHAVIOR 

sufficiently  raised,  a  change  occurs — nobody  knows  of  what 
nature — in  the  molecule,  the  solutions  become  opalescent  and 
the  albumin  may  set  to  a  solid  gel.  In  this  case  "oily"  groups 
must  be  activated  or  formed  which  were  not  active  or  did  not 
exist  before  and  their  natural  attraction  must  cause  the  gel 
formation. 

In  the  case  of  casein  solutions  in  acid  all  the  properties  of  the 
solution,  stability,  viscosity,  osmotic  pressure,  and  P.D.,  possess 
colloidal  character.  The  forces  of  attraction  between  the  mole- 
cules or  ions  of  casein  on  the  acid  side  of  the  isoelectric  point  for 
each  other  are  very  strong  and  for  the  water  molecules  compara- 
tively feeble.  In  the  case  of  casein  chloride  or  casein  phosphate 
and  to  a  lesser  extent  casein  nitrate,  they  are  just  strong  enough  to 
make  a  solution  possible ;  but  the  stability  of  the  solution  depends 
largely  on  the  forces  set  up  by  the  Donnan  equilibrium  between 
the  nascent  micellae  or  the  existing  micellae  and  the  surrounding 
solution.  In  the  case  of  casein  trichloracetate  or  casein  sulphate 
the  forces  of  mutual  attraction  between  the  casein  molecules  for 
each  other  are  so  much  greater  than  those  for  water  that  these 
two  salts  are  practically  insoluble.  On  account  of  this  great 
attraction  for  each  other  the  granules  of  casein  cannot  swell  in 
sulphuric  acid  or  trichloracetic  acid.  Solutions  of  Na  caseinate 
behave  like  crystalloidal  solutions  in  regard  to  stability  but  like 
colloidal  solutions  in  regard  to  viscosity,  P.D.,  and  osmotic 
pressure. 

This  shows  the  complications  which  may  be  due  to  the  large 
size  and  complex  constitution  of  large  molecules,  especially  of 
proteins.  The  problems  of  gel  formation  or  of  precipitation  are 
not  colloidal  problems,  they  are  a  part  of  the  more  general  prob- 
lem of  solubility.  These  problems  enter  only  in  a  secondary 
way  into  the  problem  of  colloidal  behavior,  since  the  phenomena 
of  aggregation  are  only  a  means  of  preventing  the  diffusion  of  an 
ion,  thereby  creating  the  conditions  for  the  establishment  of  a 
Donnan  equilibrium. 

We  now  understand  why  it  is  not  correct  to  define  colloidal 
solutions  as  solutions  in  which  the  ultimate  unit  is  a  micella, 
i.e.,  an  aggregate  of  molecules  or  ions.  The  colloidal  behavior  of 
solutions  of  salts  of  crystalline  egg  albumin  in  regard  to  osmotic 
pressure  and  P.D.  is  only  due  to  the  non-diffusibility  of  the  pro- 


COLLOIDAL  SUBSTANCES  285 

tein  ion  through  the  collodion  membrane  and  depends  in  no  way 
upon  the  existence  of  micellae.  The  existence  of  micellae  could 
only  diminish  the  value  of  the  osmotic  pressure  and  of  the  P.D. 
The  results  of  our  work  lead  to  the  conclusion  that  there  is  only 
one  source  of  colloidal  behavior,  namely,  the  Donnan  equilibrium, 
at  least  as  far  as  the  proteins  are  concerned.  Without  a  Donnan 
equilibrium  there  can  be  no  colloidal  behavior  of  proteins.  A 
Donnan  equilibrium  will  always  arise  when  the  diffusion  of  one 
kind  of  ions  is  blocked  while  the  diffusibility  of  oppositely  charged 
ions  is  unrestricted,  regardless  of  the  nature  of  the  block  restrict- 
ing the  diffusibility  and  regardless  of  the  nature  of  the  ion  the 
diffusion  of  which  is  prevented. 

The  writer  hopes  that  the  methods,  experimental  results,  and 
theoretical  conclusions  described  in  this  book  may  be  found  of 
use  not  only  in  the  study  of  the  colloidal  behavior  of  other 
substances  than  proteins  but  also  in  physiology.  Life  phenomena 
cannot  be  dissociated  from  colloidal  behavior,  and  the  idea  of  an 
organism  or  of  living  matter  consisting  exclusively  or  chiefly 
of  crystalloidal  material  or  material  with  purely  crystalloidal 
behavior  is  inconceivable.  Organisms  have  been  defined  as 
chemical  machines  consisting  essentially  of  colloidal  material 
capable  of  growing  and  automatically  reproducing  themselves.1 
If  this  be  true,  advance  in  physiology  will  be  chiefly  a  hit  or  miss 
game  until  science  is  in  possession  of  a  mathematical  theory  of  the 
colloidal  behavior  of  the  substances  of  which  living  matter  is 
composed.  If  Donnan's  theory  of  membrane  equilibria  furnishes 
the  mathematical  and  quantitative  basis  for  a  theory  of  colloidal 
behavior  of  the  proteins,  as  the  writer  believes  it  does,  it  may  be 
predicted  that  this  theory  will  become  one  of  the  foundations  on 
which  modern  physiology  will  have  to  rest. 

.  J.,  "The  Dynamics  of  Living  Matter,"  New  York,  1906. 


INDEX 


Adsorption  formula,  3 

theory,  10-13,  119,  157 
"Adsorption  compounds,"  88 
Aggregation  hypothesis,  15-17,  113, 

119,  241 
Alanine,  197 

Albumin,   crystalline  egg,  combina- 
tion curves  of,  46,  47 
conductivity  of,  118 
crystalloidal   and   colloidal   be- 
havior of,  278,  282 
heat  coagulation  of,  252 
influence  of  concentration  of,  on 
osmotic  pressure,  187,  188 
osmotic  pressure  of,  43-45 
P.D.  of,  145-148 
precipitation  of,  244,  252,  265 
preparation  of,  43-45 
stoichiometrical  behavior  of,  40, 

44-49,  60,  61 
titration  curves  of,  44,  60 
viscosity  of,  198-202 
Alcoholic  solutions  of  gelatin,  279 
micellae  of  gelatin  in  alcoholic 
and  aqueous  solutions,  280 
precipitation,  251-255,  258-261, 

263-264 
prevention  of  gel  formation  in, 

281 

viscosity  of,  280 
Allmand,  A.  J.,  22 
Amino-acids,  197 
Aniline,  8 

Anomalous  osmosis.  158,  164 
Arrhenius,   S.,    196,   201,   203,   204, 

212,  227,  230 
Ash-free  gelatin,  35,  36 


B 


Baker,  J.  C.,  52,  53,  222 
Bancroft,  W.  D.,  12,  110 
Beutner,  R.,  166-168 
Blood  albumin,  13,  115 
Born,  M.,  19,  118,  197 
Brakeley,  Miss,  197 
Bredig,  11 

Bugarszky,  S.,  4,  32,  41 
Burton,  E.  F.,  11,  275,  276,  277 


Cane   sugar,    influence   of,    on   vis- 
cosity, 109 
Casein,    crystalloidal   and   colloidal 

behavior  of,  284 
isoelectric  point  of,  9 
osmotic  pressure  of,  72,  236 
precipitation  of,  266-274 
preparation  of,  52,  53 
solubility  of,  71,  86,  193,  222, 

251,  266-272 
stability  of,  266 
stoichiometrical  behavior  of,  54, 

55 

swelling  of,  222-229,  267-272 
titration  curves  of,  54,  61 
viscosity  of,  86,  87,  221-230 
Cells  and  tissues,  P.D.  of,  166-168 
Chlorine  ion  potentials,  135-137 
Clark,  W.  M.,  4,  43 
Coagulation,  heat,  of  egg  albumin, 

252 
Collodion   membranes,    preparation 

of,  67 
Colloidal  behavior  and  living  matter, 

285 
causes  of,  277,  278 


287 


288 


INDEX 


Colloidal    behavior,    characteristics 

of,  1,  112,  276,  277 
solution,  2,  3,  8 
state,  2,  275-285 
substances,  275 
Colloids,  classification  of,  243 

and      crystalloids,       difference 

between,  1-6,  112,  275 
"hydrophilic,"  243 
"hydrophobic,"  243 
"lyophilic,"  243 
"lyophobic,"  243 
Combination   curves,    albumin   and 

acids,  46,  47 
gelatin  and  acids,  51 
Compton    electrometer,     120,     121, 

154,  155,  159 
Conductivity,  of  albumin  solutions, 

118 
of   gelatin    solutions,    38,    116, 

117 

Contraction,  muscular,  111 
Crystalloidal  behavior  of  proteins, 

277,  278 

and  colloidal  behavior  of,  albu- 
min, 278,  283 
casein,  284 
gelatin,  278,  283 


J) 


Dakin,  H.  D.,  63,  187,  279 
Donnan,  F.  G.,  19,  22,  119,  130 
Donnan's     membrane    equilibrium, 

12 

application    of,    127-149 
theory  of,  19-26,  123-125 


E 


Edema,  111 

Egg  albumin,  see  Albumin. 

Ehrenberg,  25 

Einstein,  A.,  196,  201,  202,  203,  210, 

211,  212,  230 
Electrical  charges  of  micellae,  9,  12, 

150-168 


Electrical  endosmose,  164,  165 

field,  migration  in,  6 
Electrolytes     in     precipitation     of 

proteins,  282 

Electrolytic  dissociation,  41 
Emulsion,  11 
Emulsoids,  243 
Euler,  198 


Fibrin,  swelling  of,  106,  107 

Field,  A.  M.,  36 

Film  formation  of  proteins,  165 

Fischer,  76,  77 

Flocculation,  see  Precipitation. 

Freundlich,  H.,  3 

Friederithal,  H.,  4,  9 


Garner,  W.  E;,  22 

Gel    formation    and    precipitation, 

difference  in,  283 
Gelatin,  calculation  of  P.D.  of,  124, 

125,  130-133 

combination  curves  of,  51 
conductivity  of,  38,  116,  117 
crystalloidal   and   colloidal  be- 
havior of,  278,  283 
curve  for  observed  P.D.-of,  122 
effects  of  salts  on  rate  of  solution 

of,  245-251 

influence  of  concentration  of, 
on  osmotic  pressure, 
184-187 

on  P.D.,  145,  146 
isoelectric  point  of,  9 
osmotic  pressure  of,  38,  68-70, 
73,     169-188,     233-235, 
256-257 
of  mixtures  of  liquid  and 

powdered,  236-238 
P.D.  of,  120-149,  256,  257 
precipitation   of,   critical  point 
of  alcohol  concentration  in, 
253-255 


INDEX 


289 


Gelatin,  precipitation  of,  from  alco- 
holic    solutions,    251-255, 
258-261,  263-264 
from  aqueous  solutions,  244, 

245 

stability  of,  243 
stoichiometrical  behavior  of,  40, 

49-52,  55-59,  62 
swelling  of,  38,  76-82,  189-194 
titration  curves  of,  50,  59,  62 
viscosity  of,  38,  82-86,  90-99, 
198,  201,  203,  204,  213-221 
of    mixtures    of    liquid    and 

powdered,  238-241 
Gelatin  suspensions,  effect  of  salts 

on,  157-166 

electrical  charge  of,  152-154 
influence  of  acid  and  alkali  on, 

155-157 

influence  of  pH  on,  155 
stability  of,  150-152 
viscosity  of,  206-212 
Glass,  3 
Globulins,  7,  8 
Glycocoll,  8,  197,  198 
Graham,  T.,  1,  2,  10,  113,  275 


H 


Hardy,  W.  B.,  6,  7,  8,  10,  11,  16,  37, 
150,  151,  155,  163,  243, 
261,  267,  274 

Hardy's  rule  of  precipitation,  144 
Hatschek,  E.,  196,  212 
Heat  coagulation,  252 
Hedestrand,  G.,  198 
Hildebrand,  J.  H.,  43,  48 
Hirschf elder,  A.  D.,  106,  111 
Hitchcock,  D.  I.,  35 
Hober,  R.,  14,  111 
Hofmeister,  F.,  13,  14,  25,  65,  76 
Hofmeister  ion  series,  13,  25,  65-87, 

99-111 

in  osmotic  pressure,  65-76 
in  swelling,  76-82,  105-107 
in  viscosity,  82-87,  99-104 
Hooke's  law,  190 
19 


Hydration  theory,  17-19,  114-119, 

130,  197,  230 
Hydrogen  ion  concentration,  effect 

of  salts  on,  101,  106 
influence  of,  on  charge  of  sus- 
pended particles,  155 
on  conductivity,  117,  118 
on  osmotic  pressure,   68-76, 

172-179,  234,  237 
on  P.D.,   122,   126-129,  131, 

134 

on  swelling,  76-82,  222,  227 
on  viscosity,  83-87,  99,  198, 
199,     207-209,     213,     216, 
225,  226,  234,  240 
Hydrogen  ion  potentials,  135-137 
"Hydrophilic"  colloids,  243 
"Hydrophobic  colloids,  243 


Isoelectric     point,,    conception     of, 

6-10 
method    of    determining    of, 

37-39 
of  casein,  9 
of  gelatin,  9 
of  oxyhemoglobin,  9 
of  proteins,  6 
of  serum  albumin,  9 
of  serum  globulin,  9 

K 

Karczag,  275 
Kohlrausch,  19,  114,  118 
Kossel,  W.,  33,  41 
Krafft,  275 
Kruger,  K.,  62 


Langmuir,  I.,  3,  33,  41,  250 
Laqueur,  E.,  17,  89 
Lewis,  G.  N.,  41 
Lewis,  W.  C.  McC.,  12 
Liebermann,  L.,  4,  32,  41 


290 


INDEX 


Lillie,  R.  S.,  14,  16,  66,  88,  89,  179 
Linder,  11,  16,  163,  261 
Loeb,  R.  F.,  193,  195,  243 
Lorenz,  R.,  19,  118,  197 
"Lyophilic"  colloids,  243 
"Lyophobic"  colloids,  243 


M 


MacDonald,  J.  S.,  166 

Manabe,  K,  69,  115 

Matula,  J.,  69,  115 

Membrane  equilibrium,  application 

of,  127-149 

theory  of,  19-26,  123-125 
Membrane  potentials,  120-149 

calculation  of,  125,  130,  131 
explanation  of  curves  of,  127- 

132 
method    of    measuring,    120- 

122 
of  solutions  of  egg  albumin, 

145-148 
action   of  neutral  salts  on, 

148 
of  solutions  of  gelatin,   120- 

149 
action  of  neutral  salts  on, 

139-144,  256,  257 
influence   of  concentration 

on,  145,  146 
influence    of  pH   on,    122, 

126-129,  131,  134 
influence  of  sign  of  charge 

on,  144 
influence    of    valency    on, 

132-135 

Membranes,    preparation    of    collo- 
dion, 67 
Mica,  3 
Micelhe,  2,  12 

as  units  of  colloidal  solutions, 

284,  285 
origin  of  electrical  charges  of, 

150-168 

Michaelis,  L.,  4,  9,  11,  37,  43,  116 
Migration  of  particles,  6-9,  37,  114 


Moore,  A.  R.,  Ill 
Mostynski,  B.,  116 

N 

Naegeli,  2,  113 

Nernst  formula,  21,  25,  124,  125,  137 

Neutral    salts,    action    of,    88-111, 

139-144;  157-166 
curves   for,    91-96,    98,    100, 

102,    104,    105,    107,    180, 

183,  217,    219,    220,    246, 
248,  249,  257,  262 

on  osmotic  pressure,  88,  179- 

184,  257,  262 
on  P.D.,  139-148 

on    precipitation,    244,    245, 

251-255,  258-261,  266-274 
on  rate  of  solution  of  gelatin, 

245-251 
on    swelling,    105-107,    228, 

229,  271-272 
on  viscosity,  90-100,  102-104, 

210-212,  217-220 
Northrop,  J.  H.,  32,  36 


Occlusion  theory  of  viscosity,  212, 

230 
Oil,  11 

Osborne,  T.  B.t  4 
Osmotic  pressure,   65-76,    169-188, 

232-242 
action  of  salts  on,  88,   179- 

184,  256,  257,  262 
curves  of,  180, 183,257,262 
curves  of,  albumin-acid  salts, 

71 

calculated,  173,  177 
casein-acid  salts,  72 
gelatin-acid  salts,  68,  73, 

174,  177,  234,  237 
metal  albuminates,  75 
effect  of  heating  of  solution 

on,  233-235 

influence,  of  cane  sugar  on,  109 
of  concentration  of  protein 
on,  184-188 


INDEX 


291 


Osmotic  pressure,  influence  of  pH 
on,  68-76,  172-179,  234, 
237 
of  valency  on,  65-76,  172- 

179,  256,  257 

of    mixtures    of    liquid    and 
powdered  gelatin,  236-238 
theory  of,  168-172 
Ostwald  viscometer,  82,  195,  200 
Ostwald,  Wo.,  76,  77 
Oxy hemoglobin,  9 


Paal,  275 

Pauli,  W.,  4.  13,  17,  18,  19,  27,  32, 
69,74,88,89,114-116,118, 
130,  197 

Pekelharing,  C.  A.,  36 
Pepsin  digestion,  36 
Perrin,  J.,  7,  151,  165 
Picton,  11,  16,  163,  261 
Platinum,  3 
Potential  differences,  between  solid 

gel  and  solution,  152-154 
of  cells  and  tissues,  166-168 
see  Membrane  potentials. 
Powis,  F.,  11 

Precipitation,  10-13,  113,  243-274 
critical   point    of    alcohol    con- 
centration in,  253-255 
effect  of  valency  in,   258-261. 

274 

of  casein,  266-274 
of  egg  albumin,  244,  252,  265 
of  gelatin,  in  alcoholic  solutions, 
251-255,  258-261,  263,  264 
in  aqueous  solutions,  244,  245 
Preparation  of  proteins,  27-36 
Procter,  H.  R.,  3,  23,  24,  25,  62,  63, 
124,  130,  143,  169,  170,  189, 
190-192,  269,  270,  272 
Proteins,  isoelectric  point  of,  9,  37- 

39 

preparation  of  pure,  27-36 
stability  of  solutions  of,  243-274 
titration  experiments  with,  40- 
64 


Quincke,  266 


Q 


R 


Reyher,  R.,  17 

Ringer,  W.  E.,  36 

Robertson,  T.  B.,  4,  25,  32,  230,  267 


Sackur,  O.,  17,  32,  89 

Schulze,  11,  16,  163,  261 

Serum  albumin,  9 

Smith,  C.  R.,  36 

Smoluchowski,   M.,    196,   204,   205. 

212 
Solubility,    of   casein,    71,    86,    193, 

222,  251,  266-274 
of  gelatin,   effect   of   salts   on, 

245-251 
S0rensen,  S.  P.  L.,  4,  9,  28,  32,  42, 

43,  45,  147,  244,  278 
Stability,  of  protein  solutions,  243- 

274 

of  suspensions,  150-152 
Stoichiometrical  behavior,  of  albu- 
min, 40,  44-49,  60,  61 
of  casein,  54,  55 
of    gelatin,    40,    49-52,    55-59, 

62 

Surface  tension,  11 
Suspensions  of  gelatin,  effect  of  salts 

on  charge  of,  157-166 
electrical  charge  of,  152-154 
influence  of  acid  and  alkali 

on,  155-157 
influence  of  pH  on  charge  of, 

155 

stability  of,  150-152 
viscosity  of,  206-212 
Suspensoids,  243 
Swelling,  76-82,  189-194 

curves  for,  38,  79,  80,  81,  222 
effect  of  salts,  105-107,  228,  229 
curves  for,  105,  107 


292 


INDEX 


Swelling,  influence  of  pH  on,  76-82, 

222,  227 
of  valency  on,    76-82,    105- 

107 

of  casein,  222-229,  267-272 
of  fibrin,  106,  107 
of  gelatin  blocks,  76 
of  powdered  gelatin,  38,  77-82 
theory  of,  23-26,  189-194 


Titration,  5,  40-64 

for  bromine,  38,  39,  55-57 
with  NaOH,  56 
Titration  curves,  albumin  in  acids, 

44,  46 

in  alkalies,  60 
casein  in  acids,  54 

in  alkalies,  61 
gelatin  in  acids,  50,  59 
in  alkalies,  62 


U 


Ultramicrons,  3 
Urea,  8 


Valency  effect,  13-15,  65-87,  99-111, 

132-135,  172-179,  256-261 

on  osmotic  pressure,   65-76, 

172-179,  256,  257 
on  P.D.,  132-135 
on  precipitation,  258-261 
on  swelling,  76-82,  105-107 
on  viscosity,  82-87,  99-104 
Van  Slyke,  L.  L.,  52,  53,  222 
van't  Hoff,  169 
Viscosity,     of     albumin     solutions, 

198-202,  205 
curves  for,  199-200 
influence  of,  concentration  on, 

200 

pH  on,  198,  199 
temperature  on,  205 
of  amino  acids,  197,  198 
of    casein     solutions,    86,    87, 
221-320 


Viscosity,  of  casein  solutions,  curves 

for,  87,  225,  262 
influence  of,  pH  on,  86,  87, 

225,  226 

valency  on,  86,  87 
of  gelatin  solutions,  82-86,  198, 

203,  204,  213-221 
curves  for,  38,  83-85,  198, 

201,  213,  215,  216,  221 
effect  of  salts  on,  90-100, 

102-104,  217 
curves  for,  91-96,  98, 
100,   102,   104,  217, 
219,  220 
effect  of  standing  on,  213- 

220 
influence  of,  cane  sugar  on, 

109 
concentration    on,    201, 

203,  204 
pH  on,  83-86,  198,  213, 

216,  221,  240 
temperature  on,  201,  215, 

219-221 

valency,  82-86,  99 
of  gelatin  suspensions,  206-212 
curves  for,  207-210 
effect  of  salts  on,  210-212 
influence  of  pH  on,  207-209 
of  mixtures  of  liquid  and  pow- 
dered gelatin,  238-241 
theory  of,  195-231 


W 


Weimarn,  von,  275 

Werner,  A.,  32,  33,  41,  42 

Wilson,  J.  A.,  3,  23,  24,  62,  63,  124, 
130,  143,  151,  170,  189,  190, 
191,  192,  269,  270,  272 

Wilson,  W.  H.,  3,  190 

Wintgen,  R.,  62 

Wood,  T.  B.,  8,  10 


Zsigmondy,  R.,  2,  3,  5,  11,  76,  77, 
113,  204,  205 


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